Question

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

slope $\frac{\mathbf{3}}{\mathbf{2}}$, passes through $\left(-\mathbf{5},\mathbf{1}\right)$

Short answer

The equation of the required straight line in slope-intercept form is $y=\frac{3}{2}x+\frac{17}{2}$.

Step-by-step solution

Step 1. State the concept

The slope intercept form of a straight-line equation is $y=mx+c$ where mis 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 $\frac{3}{2}$ and the line passes through $\left(-5,1\right)$.

Then, $m=\frac{3}{2}$ and $\left(h,k\right)=\left(-5,1\right)$.

Step 3. Write the equation

Put $m=\frac{3}{2}$ and $\left(h,k\right)=\left(-5,1\right)$ in $y-k=m\left(x-h\right)$ to get,

$y-1=\frac{3}{2}\left(x-\left(-5\right)\right)$

$y-1=\frac{3}{2}\left(x+5\right)$ (Simplify)

$y-1=\frac{3}{2}x+\frac{15}{2}$ (Distributive property)

$y-1+1=\frac{3}{2}x+\frac{15}{2}+1$ (Add 1 to both sides)

$y=\frac{3}{2}x+\frac{17}{2}$ (Simplify)

So, the required equation of the straight line in slope-intercept form is $y=\frac{3}{2}x+\frac{17}{2}$.