Q6. - 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 $\left(\mathbf{6},\mathbf{4}\right)$

Step-by-Step Solution

Answer

The equation of the required straight line in slope-intercept form is $y=0.5x+1$.

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 $\left(6,4\right)$.

Then, $m=0.5$ and $\left(h,k\right)=\left(6,4\right)$.

Step 3 – Write the equation

Put $m=0.5$ and $\left(h,k\right)=\left(6,4\right)$ in $y-k=m\left(x-h\right)$ to get,

$y-4=0.5\left(x-6\right)$

$y-4=0.5x-3$  (Distributive property)

$y-4+4=0.5x-3+4$  (Add 4 to both sides)

$y=0.5x+1$  (Simplify)

So, the required equation of the straight line in slope-intercept form is $y=0.5x+1$.