Q25. - Algebra 2

Question

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

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

Step-by-Step Solution

Answer

The equation of the required straight line in slope-intercept form is $y=-\frac{1}{2}x+\frac{7}{2}$.

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

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

Step 3 – Write the equation

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

 

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

 

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

 

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

 

$y=-\frac{1}{2}x+\frac{7}{2}$  (Simplify)

 

So, the required equation of the straight line in slope-intercept form is $y=-\frac{1}{2}x+\frac{7}{2}$.