Q30. - Algebra 2

Question

Write an equation in slope-intercept form for the line that satisfies each set of conditions.

30. passes through $\left(\mathbf{7},\mathbf{1}\right)$ and $\left(\mathbf{7},\mathbf{8}\right)$

Step-by-Step Solution

Answer

The equation of the required straight line is $x=7$. This is a vertical line and thus cannot be represented in slope-intercept form.

Step 1 – State the concept

The slope intercept form of a straight-line equation is $y=mx+c$ where $m$ is the slope and $c$ is the y-intercept.

 

The equation of a straight-line passing through the points $\left(h,k\right)$ and $\left(a,b\right)$ is given as $\frac{y-k}{x-h}=\frac{b-k}{a-h}$.

Step 2 – List the given data

It is given that the line passes through $\left(7,1\right)$ and $\left(7,8\right)$.

Then, $\left(h,k\right)=\left(7,1\right)$ and $\left(a,b\right)=\left(7,8\right)$.

Step 3 – Write the equation

Put $\left(h,k\right)=\left(7,1\right)$ and $\left(a,b\right)=\left(7,8\right)$ in $\frac{y-k}{x-h}=\frac{b-k}{a-h}$ to get,

 

$\frac{y-1}{x-7}=\frac{8-1}{7-7}$

 

$\frac{y-1}{x-7}=\frac{7}{0}$  (Simplify)

 

$\frac{x-7}{y-1}=\frac{0}{7}$  (Taking reciprocals on both sides)

 

$\frac{x-7}{y-1}=0$  (Simplify)

 

$\frac{x-7}{y-1}\left(y-1\right)=0\left(y-1\right)$  (Multiply both sides by $y-1$)

 

$x-7=0$ (Simplify)

 

$x-7+7=0+7$  (Add 7 to both sides)

 

$x=7$   (Simplify)

 

So, the required equation of the straight line is $x=7$. This is a vertical line and cannot be represented in slope-intercept form.