Q19. - Algebra 2

Question

Write an equation in slope-intercept form for each graph.

Step-by-Step Solution

Answer

The equation of the required straight line in slope-intercept form is $y=\frac{4}{5}x$.

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 clear, from the graph, that the line passes through the origin $\left(0,0\right)$ and $\left(2.5,2\right)$.

Then, $\left(h,k\right)=\left(0,0\right)$ and $\left(a,b\right)=\left(2.5,2\right)$.

Step 3 – Write the equation

Put $\left(h,k\right)=\left(0,0\right)$ and $\left(a,b\right)=\left(2.5,2\right)$ in $\frac{y-k}{x-h}=\frac{b-k}{a-h}$ to get,

 

$\frac{y-0}{x-0}=\frac{2-0}{2.5-0}$

 

$\frac{y}{x}=\frac{2}{2.5}$  (Simplify)

 

$\frac{y}{x}=\frac{4}{5}$  (Simplify)

 

$\frac{y}{x}\left(x\right)=\frac{4}{5}\left(x\right)$   (Multiply both sides by \[x\])

 

$y=\frac{4}{5}x$ (Simplify)

 

So, the required equation of the straight line in slope-intercept form is $y=\frac{4}{5}x$.