Question

A line passes through the point (-9,5) and has a slope of12 / 2Write an equation in slope-intercept form for this line.

Answer 1

The form of the slope-intercept of the linear equation is

`y=mx+b`

m is the slope

b is the y-intercept

Since the slope of the line is 2/3, then

`m=(2)/(3)`

Substitute it in the form of the equation

`y=(2)/(3)x+b`

Since the line passes through the point (-9, 5), then

Substitute x in the equation by -9 and y by 5 to find the value of b

`\begin{gathered} 5=(2)/(3)(-9)+b \\ 5=-(18)/(3)+b \\ 5=-6+b \end{gathered}`

Add 6 to both sides

`\begin{gathered} 5+6=-6+6+b \\ 11=b \end{gathered}`

Then the equation of the line is

`y=(2)/(3)x+11`