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Since it looks like this Ds question has gotten 'buried', I'm going to bump it back up with a 'nudge' about how to solve it:

When dealing with graphing and lines, it helps to organize your data using slope-intercept format:

Y = (M)(X) + B

We're given the slope of a line and one of the points that it runs through. From this, you can calculate the value of B. With the equation of the full line, you should then be able to calculate the X-intercept....

Think about this visually. A slope of – 5/3 means, among other things, right 3 spaces, down 5. If the line goes through the point (–2, 7), then it must also go through (1, 2), which is much closer to the x-intercept. Let’s think about this in the vicinity of the x-intercept.

Obviously, (1, 2) is at a height of 2 above the x-axis. Let b be the distance from (1, 0) to the x-intercept. We know –h/b must equal the slope.

Think about this visually. A slope of – 5/3 means, among other things, left 3 spaces, down 5. If the line goes through the point (–2, 7), then it must also go through (1, 2), which is must closer to the x-intercept. Let’s think about this in the vicinity of the x-intercept.

Attachment:

ppocg_img6.png

Obviously, (1, 2) is at a height of 2 above the x-axis. Let b be the distance from (1, 0) to the x-intercept. We know –h/b must equal the slope.

Now, we just have to add one to that to get the horizontal distance from the origin.

x-intercept = 2 1/5.

Answer = (B)

Hi Bunuel,

Please make me understand the below point:

A slope of – 5/3 means, among other things, left 3 spaces, down 5. If the line goes through the point (–2, 7), then it must also go through (1, 2), which is must closer to the x-intercept.

I believe, for slope - 5/3, right 3 spaces and down 5 so that the line goes through (1,2) from (-2,7) downward slope. Please explain if iam wrong.

Think about this visually. A slope of – 5/3 means, among other things, left 3 spaces, down 5. If the line goes through the point (–2, 7), then it must also go through (1, 2), which is must closer to the x-intercept. Let’s think about this in the vicinity of the x-intercept.

Obviously, (1, 2) is at a height of 2 above the x-axis. Let b be the distance from (1, 0) to the x-intercept. We know –h/b must equal the slope.

Now, we just have to add one to that to get the horizontal distance from the origin.

x-intercept = 2 1/5.

Answer = (B)

Hi Bunuel,

Please make me understand the below point:

A slope of – 5/3 means, among other things, left 3 spaces, down 5. If the line goes through the point (–2, 7), then it must also go through (1, 2), which is must closer to the x-intercept.

I believe, for slope - 5/3, right 3 spaces and down 5 so that the line goes through (1,2) from (-2,7) downward slope. Please explain if iam wrong.

Re: Line A has a slope of -5/3 and passes through the point (–2, 7). What [#permalink]

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26 May 2015, 00:55

1

This post received KUDOS

1

This post was BOOKMARKED

My attempt

I am very fond of co-ordinate geometry

Using slope intercept form of equation y=mx+c In this case y=(-5/3)x+c

We know that the line passes through (-2,7) So solving for c c=7-(5*2/3)=11/3

So equation of line is y=(-5/3)x+(11/3)

Changing the equation of line to intercept form x/(11/5) + y/(11/3) = 1

So x intercept is 11/5=2 1/5 which is B

Some theory to keep in mind

An equation of line can be represented in multiple forms 1. y=mx+c where m is the slope and c is a constant 2. x/a + y/b = 1 here a and b are the intercepts on x and y axis respectively 3. (y-y1)/(y2-y1) = (x-x1)/(x2-x1) equation of line passing through (x1,y1) and (x2,y2)

I think basis these it becomes easier to solve and one must know how to change forms of these equations quickly. All these are linear equations.
_________________

Re: Line A has a slope of -5/3 and passes through the point (–2, 7). What [#permalink]

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07 Apr 2016, 22:57

Jackal wrote:

My attempt

I am very fond of co-ordinate geometry

Using slope intercept form of equation y=mx+c In this case y=(-5/3)x+c

We know that the line passes through (-2,7) So solving for c c=7-(5*2/3)=11/3

So equation of line is y=(-5/3)x+(11/3)

Changing the equation of line to intercept form x/(11/5) + y/(11/3) = 1

So x intercept is 11/5=2 1/5 which is B

Some theory to keep in mind

An equation of line can be represented in multiple forms 1. y=mx+c where m is the slope and c is a constant 2. x/a + y/b = 1 here a and b are the intercepts on x and y axis respectively 3. (y-y1)/(y2-y1) = (x-x1)/(x2-x1) equation of line passing through (x1,y1) and (x2,y2)

I think basis these it becomes easier to solve and one must know how to change forms of these equations quickly. All these are linear equations.

Re: Line A has a slope of -5/3 and passes through the point (–2, 7). What [#permalink]

Show Tags

08 Apr 2016, 06:46

akshay4gmat wrote:

Jackal wrote:

My attempt

I am very fond of co-ordinate geometry

Using slope intercept form of equation y=mx+c In this case y=(-5/3)x+c

We know that the line passes through (-2,7) So solving for c c=7-(5*2/3)=11/3

So equation of line is y=(-5/3)x+(11/3)

Changing the equation of line to intercept form x/(11/5) + y/(11/3) = 1

So x intercept is 11/5=2 1/5 which is B

Some theory to keep in mind

An equation of line can be represented in multiple forms 1. y=mx+c where m is the slope and c is a constant 2. x/a + y/b = 1 here a and b are the intercepts on x and y axis respectively 3. (y-y1)/(y2-y1) = (x-x1)/(x2-x1) equation of line passing through (x1,y1) and (x2,y2)

I think basis these it becomes easier to solve and one must know how to change forms of these equations quickly. All these are linear equations.

HOW YOU ARE EQUATING 11/5 TO 21/5 PLEASE EXPLAIN

Hi Akshay

Just as Chetan explained.

\(= \frac{11}{5}\)

\(= \frac{(10 + 1)}{5}\)

\(= 2 \frac{1}{5}\)

Apologies for not using Latex equivalent symbols
_________________

Re: Line A has a slope of -5/3 and passes through the point (–2, 7). What [#permalink]

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14 Jul 2016, 06:55

1

This post was BOOKMARKED

Bunuel wrote:

Line A has a slope of -5/3 and passes through the point (–2, 7). What is the x-intercept of Line A?

A. 2 1/3 B. 2 1/5 C. 2 2/3 D. 2 2/5 E. 2 3/5

Kudos for a correct solution.

Point intercept form a line is y=mx+b slope = m, y intercept =b (given that x=0) x intercept =-b/m Here we know m=-5/3 ; we need to find b and we are done

lets use the equation by plugging values of x,y and m from the question stem 7=-5/3*-2 +b ==> 7=10/3+b

b=11/3

x intercept = -b/m = -11/3/-5/3=-11/-5==> 11/5 = 2 \(\frac{1}{5}\)

Answer is B
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Re: Line A has a slope of -5/3 and passes through the point (–2, 7). What [#permalink]

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05 Nov 2017, 02:45

Hi @bunnel,

Could please explain the how you arrived at x intercept.

The equation of the line is -5x-3y+11 = 0

So should the y intercept be -a/b = -5/3?

Thanks in advance! S

Jackal wrote:

My attempt

I am very fond of co-ordinate geometry

Using slope intercept form of equation y=mx+c In this case y=(-5/3)x+c

We know that the line passes through (-2,7) So solving for c c=7-(5*2/3)=11/3

So equation of line is y=(-5/3)x+(11/3)

Changing the equation of line to intercept form x/(11/5) + y/(11/3) = 1

So x intercept is 11/5=2 1/5 which is B

Some theory to keep in mind

An equation of line can be represented in multiple forms 1. y=mx+c where m is the slope and c is a constant 2. x/a + y/b = 1 here a and b are the intercepts on x and y axis respectively 3. (y-y1)/(y2-y1) = (x-x1)/(x2-x1) equation of line passing through (x1,y1) and (x2,y2)

I think basis these it becomes easier to solve and one must know how to change forms of these equations quickly. All these are linear equations.

Line A has a slope of -5/3 and passes through the point (–2, 7). What [#permalink]

Show Tags

15 Nov 2017, 12:39

1

This post received KUDOS

Bunuel wrote:

Line A has a slope of -5/3 and passes through the point (–2, 7). What is the x-intercept of Line A?

A. 2 1/3 B. 2 1/5 C. 2 2/3 D. 2 2/5 E. 2 3/5

Kudos for a correct solution.

With a slope and a point, and asked to find the x-intercept of a line, I use the slope intercept form. (It's quick).

1) Start with just the slope to construct a slope-intercept equation for the line: \(y = mx + b\), m = slope, b = y-intercept Slope = \(-\frac{5}{3}\),so \(y = -\frac{5}{3}x + b\)

2) Next, plug in the given point (-2,7) to find \(b\) \(7 = -\frac{5}{3}(-2) + b\) \(7 = \frac{10}{3} + b\) \((7 - \frac{10}{3}) = \frac{11}{3} = b\)

3) Plug \(b\) in. The line's equation is now \(y = -\frac{5}{3}x + \frac{11}{3}\)

4) Set y equal to 0 to find x-intercept \(0 = -\frac{5}{3}x + \frac{11}{3}\) \(\frac{5}{3}x=\frac{11}{3}\) \(x=\frac{11}{3}*\frac{3}{5}=\frac{11}{5}\) \(=2\frac{1}{5}\)

Answer B

Shiv2016 , yes, it's correct. I had to grin, though (with relief!) because I have done what you did . . . There is no need to find the slope. It's given.