Question

Find the equation of the line with slope = -9 and passing through (-9,5) Write equation in point - slope AND slope- intercept forms.

Answer 1

The point-slope form of the linear equation is

`y-y_1=m(x-x_1)`

Where:

m is the slope

(x1, y1) is a point on the line

Since the slope of the line is -9, then

m = -9

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

x1 = -9 and y1 = 5

Substitute them in the form of the equation above

`\begin{gathered} m=-9,x_1=-9,y_1=5 \\ y-5=-9(x-\lbrack-9\rbrack) \\ y-5=-9(x+9) \end{gathered}`

The point-slope form is y - 5 = -9(x + 9)

The slope-intercept form of the linear equation is

`y=mx+b`

Where:

m is the slope

b is the y-intercept

Since the slope of the line is -9, then

m = -9

Substitute it in the form of the equation above

`\begin{gathered} m=-9 \\ y=-9x+b \end{gathered}`

To find b use the given point on the line (-9, 5)

Substitute x in the equation by -9 and y by 5

`\begin{gathered} x=-9,y=5 \\ 5=-9(-9)+b \\ 5=81+b \end{gathered}`

Subtract 81 from both sides to find b

`\begin{gathered} 5-81=81-81+b \\ -76=b \end{gathered}`

Substitute b in the equation by -76

`\begin{gathered} y=-9x+(-75) \\ y=-9x-76 \end{gathered}`

The slope-intercept form is y = -9x -76