Q. 27 - Algebra 2

Question

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

slope $-\mathbf{0}.\mathbf{5}$, passes through $\left(\mathbf{2},-\mathbf{3}\right)$

Step-by-Step Solution

Answer

The equation of the required straight line in slope-intercept form is $y=-0.5x-2$.

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 $-0.5$ and the line passes through $\left(2,-3\right)$.

Then, $m=-0.5$ and $\left(h,k\right)=\left(2,-3\right)$.

Step 3. Write the equation

Put $m=-0.5$ and $\left(h,k\right)=\left(2,-3\right)$ in $y-k=m\left(x-h\right)$ to get,

 

$y-\left(-3\right)=-0.5\left(x-2\right)$

 

$y+3=-0.5\left(x-2\right)$  (Simplify)

 

$y+3=-0.5x+1$  (Distributive property)

 

$y+3-3=-0.5x+1-3$  (Subtract 3 from both sides)

 

$y=-0.5x-2$  (Simplify)

 

So, the required equation of the straight line in slope-intercept form is $y=-0.5x-2$.