Q7. - Algebra 2

Question

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

7. slope $-\frac{\mathbf{3}}{\mathbf{4}}$, passes through $\left(\mathbf{2},\frac{\mathbf{1}}{\mathbf{2}}\right)$

Step-by-Step Solution

Answer

The equation of the required straight line in slope-intercept form is $y=-\frac{3}{4}x+2$.

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 $-\frac{3}{4}$ and the line passes through $\left(2,\frac{1}{2}\right)$.

Then, $m=-\frac{3}{4}$ and $\left(h,k\right)=\left(2,\frac{1}{2}\right)$.

Step 3 – Write the equation

Put $m=-\frac{3}{4}$ and $\left(h,k\right)=\left(2,\frac{1}{2}\right)$ in $y-k=m\left(x-h\right)$ to get,

$y-\frac{1}{2}=-\frac{3}{4}\left(x-2\right)$

$y-\frac{1}{2}=-\frac{3}{4}x+\frac{3}{2}$  (Distributive property)

$y-\frac{1}{2}+\frac{1}{2}=-\frac{3}{4}x+\frac{3}{2}+\frac{1}{2}$  (Add $\frac{1}{2}$ to both sides)

$y=-\frac{3}{4}x+2$  (Simplify) 

So, the required equation of the straight line in slope-intercept form is $y=-\frac{3}{4}x+2$.