Question

Use the point -slope formula and the given points to write linear equation in slope-intercept form.(4,-1),(6,-7)

Answer 1

Given a line l, if the following points

`\lbrace(x_1,y_1),(x_2,y_2)\rbrace`

belongs to the line l, the slope m of this line is given by the following formula

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

Using this formula in our problem, we have

`m=((-7)-(-1))/((6)-(4))=(-7+1)/(6-4)=(-6)/(2)=-3`

The slope of our line is - 3.

The slope intercept form is

`y=mx+b`

where m represents the slope and b the y-intercept.

We already calculated the slope, if we substitute its value on this form and evaluate one of the points, we can solve the equation for b.

`\begin{gathered} (-1)=(-3)(4)+b \\ -1=-12+b \\ b=11 \end{gathered}`

Our line equation is

`y=-3x+11`