Question

19. Write the slope-intercept form of the line described in the following:Perpendicular to x + 4y = 12 and passing through (7, -3)

Answer 1

The Slope-Intercept form of an equation of the line is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

Given this line:

`x+4y=12`

You need to solve for "y" in order to write it in Slope-Intercept form:

`\begin{gathered} 4y=-x+12 \\ y=(-1)/(4)x+(12)/(4) \\ \\ y=-(1)/(4)x+3 \end{gathered}`

So you can identify that the slope of that line is:

`m_1=-(1)/(4)`

By definition, the slopes of perpendicular lines are opposite reciprocals. Then, you can determine that the slope of the other line is:

`m_2=4`

Knowing that it passes through this point:

`\mleft(7,-3\mright)`

You can substitute the coordinates into the equation and solve for "b":

`\begin{gathered} -3=4(7)+b \\ -3-28=b \\ b=-31 \end{gathered}`

Knowing the value of "b" and knowing the slope, you can determine that the equatio of the line in Slope-Intercept for