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=(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=(5-2)/(1-(-3))=(3)/(4)`

`y=(3)/(4)x+b`

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

`5=(3)/(4)(1)+b\\\\5=(3)/(4)+b\qquad|-(3)/(4)\\\\b=4(1)/(4)`

Answer:
`y=(3)/(4)x+4(1)/(4)`