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 $\left(\mathbf{0},\mathbf{4}\right)$

Short answer

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

Step-by-step solution

– 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 $y-k=m\left(x-h\right)$.

– 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 $\left(h,k\right)=\left(0,4\right)$.

– 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 $y=0.25x+4$.