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

User Nyxtom
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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

User Pankaj Chauhan
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