Question

Find the equation of a line with given slope and containing given point. Write the equation in sole-intercept m= -7/2, point (-8,-4)

Answer 1

Given:

There are given that the slope and the point:

$\begin{gathered} m=-\frac{7}{2} \\ point:\left(-8,-4\right) \end{gathered}$

Explanation:

To find the equation, first, we need to see the formula for slope-intercept form:

So,

From the slope-intercept formula;

$y=mx+b$

Where,

$\begin{gathered} m=-\frac{7}{2} \\ \lparen x,y)=\left(-8,-4\right) \end{gathered}$

Now,

We need to find the value of b by using given information:

So,

Put all the given values into the given slope-intercept form:

$\begin{gathered} y=mx+b \\ -4=-\frac{7}{2}\left(-8\right)+b \\ -4=28+b \\ b=-32 \end{gathered}$

Then,

Put the value of b and m into the slope-intercept form;

So,

$\begin{gathered} y=mx+b \\ y=-\frac{7}{2}x+\left(-32\right) \\ y=-\frac{7}{2}x-32 \end{gathered}$

Final answer:

Hence, the equation of a line is shown below;

$y=-\frac{7}{2}x-32$