Question

How do you write the equation of a line through (5,-2) and (0,3)?

Answer 1

`y=-x+3`

Explanation:

We can either find the slope and a point (point-slope form), or find the slope and the y intercept (slope-intercept form). We are given 2 points, from which we can find the slope, and one of those points is on the y axis `(0,3)`.

Use slope-intercept form `y=mx+b`

Intercept given is at `(0,3)`

Slope :
`m=(y_2-y_1)/(x_2-x_1)`
`m=((3)-(-2))/((0)-(5))`
`m=(5)/(-5)`
`m=-1`

Equation:
`y=(-1)x+(3)`
`y=-x+3`