Question

What is the slope intercept from of the equation of the line that that passes through the points (-3, 2) and (1, 5)

Answer 1

The slope-intercept form of a line:

$y=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\to slope\\\\b\to y-intercept$

We have:

$(-3,\ 2)\to x_1=-3,\ y_1=2\\(1,\ 5)\to x_2=1,\ y_2=5$

Substitute:

$m=\dfrac{5-2}{1-(-3)}=\dfrac{3}{4}$

$y=\dfrac{3}{4}x+b$

Put the values of coordinates of the point (1, 5) to the equation of a line:

$5=\dfrac{3}{4}(1)+b\\\\5=\dfrac{3}{4}+b\qquad|-\dfrac{3}{4}\\\\b=4\dfrac{1}{4}$

Answer: $y=\dfrac{3}{4}x+4\dfrac{1}{4}$