Q33. - Algebra 2

Question

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

$\mathbf{x}$-intercept $-\mathbf{4}$, $\mathbf{y}$-intercept $\mathbf{4}$

Step-by-Step Solution

Answer

The equation of the required straight line in slope-intercept form is $y=x+4$.

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 $x$-intercept is the value of $x$ when $y=0$ and the $y$-intercept is the value of $y$ when $x=0$.

So, if the $x$-intercept is $a$, then the line passes through $\left(a,0\right)$ and if the $y$-intercept is $b$, then the line passes through $\left(0,b\right)$.

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 $x$-intercept is $-4$ and the $y$-intercept is $4$. Then, the line passes through $\left(-4,0\right)$ and $\left(0,4\right)$.

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

Step 3 – Write the equation

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

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

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

$\frac{y}{x+4}=1$  (Simplify)

$\frac{y}{x+4}\left(x+4\right)=1\left(x+4\right)$  (Multiply both sides by $x+4$) 

$y=x+4$   (Simplify)

So, the required equation of the straight line in slope-intercept form is $y=x+4$.