Question

what is an equation of the line that passes through the points (-4,-6) and (4,4)

Answer 1

Equation of a line

The slope-intercept form of the line can be written as follows:

$y=mx+b$

Where m is the slope and b is the y-intercept

We have two points through which the line passes. If we substitute them into the equation, we can find the values of m and b.

Using the point (-4,-6):

$\begin{gathered} -6=m(-4)+b \\ \text{Operate:} \\ -6=-4m+b \end{gathered}$

Using the point (4,4):

$\begin{gathered} 4=m(4)+b \\ \text{Operate:} \\ 4=4m+b \end{gathered}$

Subtract the second equation from the first equation:

$\begin{gathered} -6-4=-4m-4m+b-b \\ \text{Simplify:} \\ -10=-8m \end{gathered}$

Solve for m:

$m=-\frac{10}{-8}=\frac{5}{4}$

Substituting into the second equation:

$\begin{gathered} 4=4\cdot\frac{5}{4}+b \\ \text{Operate:} \\ 4=5+b \\ \text{Solve:} \\ b=-1 \end{gathered}$

Finally, the equation of the required line is:

$y=\frac{5}{4}x-1$