The equation of a straight line containing the points (10,100) and (15

We can use the slope-intercept form of a line equation:
\(y = mx + b\)
\(m\) = slope
\(b\) = y-intercept

The answers are all in this form.

1) Find the slope of line from coordinates of the two given points:

\(\frac{rise}{run}=\frac{y2-y1}{x2-x1}=\frac{(100-60)}{10-15}=\frac{40}{-5}= -8 =\) slope

Insert the (-8) where \(m\) is in \(y = mx+b\)

\(y = -8x + b\)

2. Now find \(b.\)
Use the (x,y) coordinates from one of the two given points.
Substitute them into what we have so far:
\(y = -8x + b\)

We can substitute because every point on a line (i.e., its coordinates) will satisfy the equation for the line.

I will use (x,y) = (10,100) to find b, the y-intercept:

\(100 = -8(10) + b\)
\(100 + 80=b\)
\(b = 180\)

\(b\) is positive, so in the original equation, the + sign on the RHS stays the same

We found \(m\) and \(b\).
For this question, all we have to do now is put those two values back into the slope-intercept equation, the one we started with.

3) Final: \(y = -8x + 180\)

Answer A