Find the Linear Equation Through Points (-2,-6) and (4,12): Two-Point Form

Question

Find the equation of the line passing through the two points $(-2,-6),(4,12)$

00:00 Find the algebraic representation of the function

00:04 Use the formula to find the slope using 2 points

00:11 In each point, the left number represents X-axis and the right Y

00:17 Plot the points according to the data and find the slope

00:30 This is the line's slope

00:35 Now use the line equation

00:39 Plot the point according to the data

00:44 Input the slope, and solve to find the intersection point (B)

00:59 Isolate the intersection point (B)

01:05 This is the intersection point with the Y-axis

01:11 Now input the intersection point and slope into the line equation

01:19 And this is the solution to the question

In the first step, we'll find the slope using the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

We'll substitute according to the given points:

$m=\frac{12-(-6)}{4-(-2)}$

$m=\frac{18}{6}=3$

Now we'll choose the point (4,12) and use the formula:

$y=mx+b$

$12=3\times4+b$

$12=12+b$

$b=0$

We'll substitute the data into the formula to find the equation of the line:

$y=3x$

$y=3x$