Q31. - Algebra 2

Question

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

31. passes through $\left(-\mathbf{4},\mathbf{0}\right)$ and $\left(\mathbf{3},\mathbf{0}\right)$

Step-by-Step Solution

Answer

The equation of the required straight line in slope-intercept form is $y=0$, that is, the x-axis.

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 $\left(-4,0\right)$ and $\left(3,0\right)$.

Then, $\left(h,k\right)=\left(-4,0\right)$ and $\left(a,b\right)=\left(3,0\right)$.

Step 3 – Write the equation

Put $\left(h,k\right)=\left(-4,0\right)$ and $\left(a,b\right)=\left(3,0\right)$ in $\frac{y-k}{x-h}=\frac{b-k}{a-h}$ to get,

 

$\frac{y-0}{x-\left(-4\right)}=\frac{0-0}{3-\left(-4\right)}$

 

$\frac{y}{x+4}=\frac{0}{3+4}$  (Simplify)

 

$\frac{y}{x+4}=\frac{0}{7}$  (Simplify)

 

$\frac{y}{x+4}=0$  (Simplify)

 

$\frac{y}{x+4}\left(x+4\right)=0\left(x+4\right)$  (Multiply both sides by $x+4$)

 

$y=0$   (Simplify)

 

So, the required equation of the straight line in slope-intercept form is $y=0$, that is, the x-axis.