Question

Find the slope of a line that is through the points (5,-3) and (2, 1). Find the y intercept and then write it in slope intercept form. y= mx + b

Answer 1

Given the points: (5,-3) and (2, 1)

We have that the equation is of the form y = mx + b, where m is the slope and b is the y-intercept. So

- For the slope:

$m=\frac{y2-y1}{x2-x1}=\frac{1-(-3)}{2-5}=\frac{1+3}{-3}=-\frac{4}{3}$

- For the y-intercept:

we use the point (2,1)

$\begin{gathered} y=mx+b \\ 1=-\frac{4}{3}(2)+b \\ 1=-\frac{8}{3}+b \\ 1+\frac{8}{3}=-\frac{8}{3}+b+\frac{8}{3} \\ b=\frac{11}{3} \end{gathered}$

And the equation is:

$y=-\frac{4}{3}x+\frac{11}{3}$

Answer:

$y=-\frac{4}{3}x+\frac{11}{3}$