Q24. - Algebra 2

Question

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

24. slope $\mathbf{0}.\mathbf{25}$, passes through $\left(\mathbf{0},\mathbf{4}\right)$

Step-by-Step Solution

Answer

The equation of the required straight line in slope-intercept form is $y=0.25x+4$.

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 equation of a straight-line having slope $m$ and passing through the point $\left(h,k\right)$ is given as $y-k=m\left(x-h\right)$.

Step 2 – List the given data

It is given that the slope of the line is $0.25$ and the line passes through $\left(0,4\right)$.

Then, $m=0.25$ and $\left(h,k\right)=\left(0,4\right)$.

Step 3 – Write the equation

Put $m=0.25$ and $\left(h,k\right)=\left(0,4\right)$ in $y-k=m\left(x-h\right)$ to get,

 

$y-4=0.25\left(x-0\right)$

 

$y-4=0.25x$  (Simplify)

 

$y-4+4=0.25x+4$ (Add 4 to both sides)

 

$y=0.25x+4$  (Simplify)

 

So, the required equation of the straight line in slope-intercept form is $y=0.25x+4$.