Answer:
y = -x + 4
Step-by-step explanation:
We are given the points (-4, 8) and (1,3)
We want to write the equation of the line that contains these 2 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
We need to first find the slope of the line
The slope (m) 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
Even though we have 2 points, let's label the values of the points to avoid confusion & mistakes while calculating
[tex]x_1 = -4\\y_1=8\\x_2=1\\y_2=3[/tex]
Now substitute these values into the formula (note: the formula has SUBTRATION, and we have NEGATIVE values).
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{3-8}{1--4}[/tex]
Simplify
m=[tex]\frac{3-8}{1+4}[/tex]
m=[tex]\frac{-5}{5}[/tex]
Divide
m = -1
The slope of the line is -1.
Here is our line so far:
y = -x + b (when -1 is the coefficient in front of a variable, just writing a minus sign in front of the variable is sufficient).
Now we need to find b
As the equation passes through the points (-4, 8) and (1, 3), we can use either one of them to help solve for b.
Taking (1, 3) for example:
Substitute 1 as x and 3 as y.
3 = -(1) + b
Multiply
3 = -1 + b
Add 1 to both sides
4 = b
Substitute 4 as b in the equation
y = -x + 4
Topic: finding the equation of the line
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