Mathematics, 06.11.2019 12:31 frank2010

What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?

What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6

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Answer from: krystalhurst97

The equation of the line which is perpendicular to the given line and has an -intercept of is $y=\dfrac{4x}{3}-8$ i.e., $\fbox{\begin\\\ \bf{option C}\\\end{minispace}}$ .

Further explanation:

From the image attached in the question it is observed that there is a line plotted in the graph which passes through the points (-4,4) and (4,-2) .

The objective is to determine the equation of a line which has an -intercept of and the line is perpendicular to the line formed by the joining the points (-4,4) and (4,-2) .

Step1: Obtain the slope of the line given in the graph.

From the given graph it is observed that the line passes through the points (-4,4) and (4,-2) .

The slope of a line which passes through the points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is calculated as follows:

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$

To obtain the slope of the line, substitute for $x_{1}$ , for $x_{2}$ , for $y_{1}$ and for $y_{2}$ in the above equation.

$\begin{aligned}m&=\dfrac{-2-4}{4+4}\\&=\dfrac{-3}{4}\end{aligned}$

Therefore, the slope of the line given in the graph is $\dfrac{-3}{4}$ .

Express the slope of the line as $\fbox{\begin\\\ \math m_{1}=\dfrac{-3}{4}\\\end{minispace}}$

Step2: Obtain the slope of the perpendicular line.

Consider the slope of the perpendicular line as $m_{2}$ .

The product of slope of two mutually perpendicular line is always equals to .

As per the above statement the equation formed is as follows:

$\fbox{\begin\\\ \math m_{1}\times m_{2}=-1\\\end{minispace}}$

To obtain the value of $m_{2}$ substitute $\dfrac{-3}{4}$ for $m_{1}$ in the above equation.

$\dfrac{-3}{4}\times m2=-1\\m_{2}=\dfrac{4}{3}$

Therefore, the slope of the perpendicular line is $\fbox{\begin\\\ \math m_{2}=\dfrac{4}{3}\\\end{minispace}}$ .

Step3: Obtain the equation of the perpendicular line.

It is given that the -intercept of the perpendicular line is .

This implies that the perpendicular line passes through the point (6,0) .

Use the slope point form to obtain the equation of the perpendicular line.

The slope intercept form of a line which passes through the point $(x_{1},y_{1})$ and slope as $m_{2}$ is as follows:

$\fbox{\begin\\\ \math (y-y_{1})=m_{2}(x-x_{1})\\\end{minispace}}$

Substitute $\dfrac{4}{3}$ for $m_{2}$ , for $x_{1}$ and for $y_{1}$ in the above equation.

$\begin{aligned}(y-0)&=\dfrac{4}{3}(x-6)\\y&=\dfrac{4x}{3}-8\end{aligned}$

Therefore, the equation of the perpendicular line is $\fbox{\begin\\\ \math y=\dfrac{4x}{3}-8\\\end{minispace}}$ .

Thus, the equation of the line which is perpendicular to the given line and has an -intercept of is $y=\dfrac{4x}{3}-8$ i.e., option C.

Learn more:

1.A problem to complete the square of quadratic function

2.A problem to determine the slope intercept form of a line

3.Inverse function

Answer details

Grade: High school

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: Geometry, coordinate geometry, lines, equation, intercept, x-intercept, slope, slope point form, perpendicular, y=4x/3-6, slope intercept form, (y-y1)=m2(x-x1).

Answer from: Quest

step-by-step explanation:

Answer from: Quest

Two because two of one thing is two.

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