Write an equation in slope-intercept form for the line that passes through the points (6, −3) and (0, 2).

Answer 1

The first thing you want to find is the slope for the m in the y=mx+b equation.

You can find the slope with the rise/run format.

Rise/Run = (y₁+y₂)/(x₁+x₂), where (x₁,y₁) (x₂,y₂) are any two points on our line.

Given the points (6,-3) and (0,2)

x₁=6

x₂=0

y₁=-3

y₂=2

Using this, you get (-3-2)/(6-0)= -5/6

Now that we have an m, we can move on to solve for b, the y-axis intercept. This is the point on the line where you have (0,b). We are given a point that looks like this, we have (0,2). 2 is in the place where b should be, so we know b=2. Given that we know m= -5/6 and b=2, we can then write the equation

y=(-5/6)x+2

Because we only have x and y left, this is our answer.

Answer 2

Start with two-point form

(y + 3) / (x - 6) = (2 + 3) / (0 - 6)

Can you simplify and convert to slope-intercept form?