Q23. - Algebra 2

Question

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

Slope $\mathbf{3}$, passes through $\left(\mathbf{0},-\mathbf{6}\right)$

Step-by-Step Solution

Answer

The equation of the required straight line in slope-intercept form is $y=3x-6$.

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 $3$ and the line passes through $\left(0,-6\right)$.

Then, $m=3$ and $\left(h,k\right)=\left(0,-6\right)$.

Step 3 – Write the equation

Put $m=3$ and $\left(h,k\right)=\left(0,-6\right)$ in $y-k=m\left(x-h\right)$ to get,

 

$y-\left(-6\right)=3\left(x-0\right)$

 

$y+6=3x$   (Simplify)

 

$y+6-6=3x-6$  (Subtract 6 from both sides)

 

$y=3x-6$  (Simplify)

 

So, the required equation of the straight line in slope-intercept form is $y=3x-6$.