Answer:
y = 2x + 6
Step-by-step explanation:
We are given that a line runs through the points (-4,-2) and (-2,2).
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is written as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name.
First, we need to find the slope of the line.
The slope can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
Even though we have two points, let's label the values of the points to avoid confusion & mistakes.
[tex]x_1=-4\\y_1=-2\\x_2=-2\\y_2=2[/tex]
Now let's find the slope (remember: the formula has subtraction):
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{2--2}{-2--4}[/tex]
This can be simplified:
m=[tex]\frac{2+2}{-2+4}[/tex]
Add the numbers together.
m=[tex]\frac{4}{2}[/tex]
Divide.
m = 2
The slope of the line is 2.
We can substitute this into the equation for m.
Here is the equation of the line so far:
y = 2x + b
We now need to find b.
As the equation passes through both (-4, -2) and (-2, 2), we can use either one of them to help solve for b.
Taking (-4, -2) for instance:
Substitute -4 as x and -2 as y in the equation we have.
-2 = 2(-4) + b
Multiply.
-2 = -8 + b
Add 8 to both sides.
6 = b
Substitute 6 as b into the equation.
y = 2x + 6
Topic: finding the equation of the line (slope-intercept form)
See more: https://brainly.com/question/25163526
