Answer:
y = -3x -1
Step-by-step explanation:
Hi there!
We are given a line on a coordinate grid, with 2 marked points, (-1, 2) and (1, -4)
We can use these points to help find the equation of the line, which we can write 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 of the line
The formula for the slope calculated from 2 points is [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 help avoid confusion.
[tex]x_1=-1\\y_1=2\\x_2=1\\y_2=-4[/tex]
Now substitute these values into the formula to find the slope
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-4-2}{1--1}[/tex]
Simplify
m=[tex]\frac{-4-2}{1+1}[/tex]
m=[tex]\frac{-6}{2}[/tex]
Divide
m= -3
The slope of the line is -3
We can substitute this into the formula.
Here's our line so far:
y = -3x + b
Now we need to find b
As the equation passes through the points (-1, 2) and (1, -4), we can use either one to find the value of b
Taking (-1, 2) for example:
Substitute -1 as x and 2 as y.
2 = -3(-1) + b
multiply
2 = 3 + b
Subtract 3 from both sides
-1 = b
Substitute -1 as b.
y = -3x - 1
Hope this helps!
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