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

Question

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 .

EMPOWERgmatRichC · Answer

Hi All,

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....

GMAT assassins aren't born, they're made,
Rich

Temurkhon · Answer

slope -5/3 and point (-2;7), so equation is

7=(-5/3)*-2+b => b=11/3

to find X intercept, rewrite the equation

0=(-5/3)*x+11/3 => x=11/5=2 1/5

B

peachfuzz · Answer

Here is my algebraic approach:
 y = (-5/3)x + b
7 = (-5/3)(-2) + b
b = 11/3

0 = (-5/3)x + 11/3
x = 11/5 or 2 1/5

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: 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. https://gmatclub.com/forum/download/file.php?id=26029 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. h/b = 5/3 --> 2/b = 5/3. 5b = 6 --> b = 6/5 = 1 1/5. Now, we just have to add one to that to get the horizontal distance from the origin. x-intercept = 2 1/5. Answer = (B) ppocg_img6.png

balamoon · Answer

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.

Thanks

Bunuel · Answer

Yes, that's true. Edited. Thank you.

Jackal · Answer

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.

kasturi72 · Answer

With the equation y=mx+c we get 
7=10/3 + c 
So c = 11/3

To find the x intercept put y=0 in the equationy=mx+c

0= -5/3 x +11/3
Multiplying by 3 throughout 
-11 = -5x
So x=11/5
Which is 2 1/5

akshay4gmat · Answer

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

chetan2u · Answer

Hi here 11/5 is not 21/5 BUT  2 \frac{1}{5} that is 2 and 1/5..
 2 + \frac{1}{5} = \frac{(10+1)}{5} =\frac{11}{5}

Jackal · Answer

Hi Akshay Just as Chetan explained. = \frac{11}{5} = \frac{(10 + 1)}{5} = 2 \frac{1}{5} Apologies for not using Latex equivalent symbols

LogicGuru1 · Answer

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

mohitkhanna.31 · Answer

slope m= -5/3 and point (-2;7), so equation is

y=mx+b

We need to find b
7=(-5/3)*-2+b
7-10/3=b

b=11/3
to find x intercept, rewrite the equation

0=(-5/3)*x+11/3 => x=11/5

Answer B

Press +1 Kudos if you like my answer :-D

shinrai15 · Answer

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

Shiv2016 · Answer

Is this solution fine?

y= mx+c
y= -5/3*x +c

Using formula to find slope:
(7-y)/(-2-x) = -5/3

3(7-y)= -5(-2-x)

21-3y= 10+5x

5x+3y= 11

To find x-intercept, plug y= 0

x= 11/5

JeffTargetTestPrep · Answer

The equation of Line A is y = (-5/3)x + b.

Let’s now plug in (-2,7) and determine b:

7 = (-5/3)(-2) + b

7 = 10/3 + b

Multiplying by 3, we have:

21 = 10 + 3b

11 = 3b

11/3 = b

Thus, we have:

y = (-5/3)x + 11/3

We can substitute 0 for y to determine the x-intercept, and we have:

0 = (-5/3)x + 11/3

-11/3 = -5x/3

-11 = -5x

x = -11/-5 = 11/5 = 2 1/5

Answer: B

generis · Answer

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.

shinrai , you wrote Mmm, no. The y-intercept is 11/3. -5/3 is the slope. You were quoting Jackal , who wrote, "So equation of line is y=(-5/3)x+(11/3)" Jackal got the x-intercept by setting y equal to 0: 0 = (-5/3)x+(11/3) \frac{5}{3}x = \frac{11}{3} x=\frac{11}{3} * \frac{3}{5}=\frac{11}{5} The line crosses the x-axis at \frac{11}{5} (and when it crosses the x-axis, y = 0) You used this equation for the line: -5x-3y+11 = 0. (A more standard form is 5x + 3y = 11.) It doesn't matter which form of equation you use; to find the y-intercept, set x = 0. (x IS zero when the line crosses the y-axis.) Your way: -5x - 3y + 11 = 0 (-5)(0) -(3)(y) + 11 = 0 -3y = -11 y = \frac{11}{3} Hope it helps.

sumert · Answer

if someone is wondering why the second equation is equal to zero- it is because while calculating X intercept, Y will be 0.

bumpbot · Answer

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

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