Answer:
y=2x+4
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the points (-5, -6) and (4, 12)
The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
First, let's find the slope of the line
The formula for the slope calculated from two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where ([tex]x_1[/tex], [tex]y_1[/tex]) and ([tex]x_2[/tex], [tex]y_2[/tex]) are points
We have everything needed to calculate the slope, but let's label the values of the points to avoid any confusion
[tex]x_1[/tex]=-5
[tex]y_1[/tex]=-6
[tex]x_2[/tex]=4
[tex]y_2[/tex]=12
Now substitute into the formula (remember: the formula has SUBTRACTION in it)
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{12--6}{4--5}[/tex]
Simplify
m=[tex]\frac{12+6}{4+5}[/tex]
Add
m=[tex]\frac{18}{9}[/tex]
Divide
m=2
So the slope of the line is 2
Here is the equation so far:
y=2x+b
We need to find b
As the line will pass through both (-5, -6) and (4, 12), we can use the values of either one to solve for b
Let's take (4, 12) for instance
Substitute 4 as x and 12 as y
12=2(4)+b
Multiply
12=8+b
Subtract 8 from both sides
4=b
Substitute 4 as b in the equation
y=2x+4
Hope this helps!
