Question

What is the slope-intercept equation of the line below?(0,3) (4,-2)

Answer 1

The slope-intercep form is

`y=mx+b`

where m is the slope and b the y-intercept. We can find m by means of the following formula

`m=(y_2-y_1)/(x_2-x_1)`

where these values come from the given points,

`\begin{gathered} (x_1,y_1)=(0,3) \\ (x_2,y_2)=(4,-2) \end{gathered}`

Then, by substituting these values into the slope formula, we get

`m=(-2-3)/(4-0)`

which gives

`m=-(5)/(4)`

Then, our line equation has the form

`y=-(5)/(4)x+b`

Now, we can find b by subtituting one of the given point into our last equation, that is, If we substitute point (0,3) we obtain

`\begin{gathered} 3=-(5)/(4)(0)+b \\ 3=b \end{gathered}`

Then, the line equation in slope-intercept form is

`y=-(5)/(4)x+3`