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Answer:
y = 2x + 10
Step-by-step explanation:
Hi there!
We are given the points (-7, -4) and (-6, -2) and we want to write the equation of the line that passes through these points in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
First, we need to find the slope (m) of the line
The slope can be calculated from 2 points 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
We have everything we need to find the slope, but let's label the values of the points to avoid any confusion & and mistakes
[tex]x_1= -7\\y_1=-4\\x_2=-6\\y_2=-2[/tex]
Substitute these values into the formula (note: remember that the formula has subtraction in it!)
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-2--4}{-6--7}[/tex]
Simplify
m=[tex]\frac{-2+4}{-6+7}[/tex]
Add the numbers
m=[tex]\frac{2}{1}[/tex]
Divide
m=2
The slope of the line is 2
We can substitute that in:
y = 2x + b
Now we need to find b
As the equation passes through both (-7,-4) and (-6,-2), we can use either point to help solve for b
Taking (-6, -2) for example:
Substitute -6 as x and -2 as y into the equation.
-2 = 2(-6) + b
Multiply
-2 = -12 + b
Add 12 to both sides
-2 = -12 + b
+12 +12
___________
10 = b
Substitute 10 as b.
y = 2x + 10
Hope this helps!
Topic: Finding the equation of a line
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