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

$m=\frac{y_2-y_1}{x_2-x_1}$

Using this formula in our problem, we have

$m=\frac{(-7)-(-1)}{(6)-(4)}=\frac{-7+1}{6-4}=\frac{-6}{2}=-3$

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

$y=-3x+11$