Answer:
y = [tex]\frac{11}{13}[/tex] x + [tex]\frac{36}{13}[/tex]
Step-by-step explanation:
First, find the slope of the line passing through the points
Then find the y-intercept of the line
Then construct the formula
1. find the slope
remember the formula
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] is used to find the slope
now plug in the given points
(5, 7)
(-8, -4)
[tex]x_{1} = 5\\y_{1} = 7\\x_{2} = -8 \\y_{2} = -4[/tex]
[tex]\frac{(-4) - (7)}{(-8) - (5)}[/tex]
simplify and solve
= [tex]\frac{-11}{-13}[/tex]
= [tex]\frac{11}{13}[/tex]
2. find the y-intercept
remember the base formula for a line
y= mx + b
where m is the slope and b is the y-intercept
we know the slope, so now plug in one of the given coordinates for a point on the line and slove to find the y-intercept
y = mx + b
y = [tex]\frac{11}{13}[/tex]x + b
use the first set of given coordinates for a point on this line: (5, 7)
7 = [tex]\frac{11}{13}[/tex] * 5 + b
solve by inverse operations and simplifying
7 = [tex]\frac{55}{13}[/tex] + b
[tex]\frac{36}{13}[/tex] = b
3. construct the formula
now we know the slope and the y-intercept, all we have to do now is substitute it into the base formula for a line:
y = mx + b
where m is the slope and B is the y-intercept
we found that
m = [tex]\frac{11}{13}[/tex]
and
b = [tex]\frac{36}{13}[/tex]
so that means the equation is
y = [tex]\frac{11}{13}[/tex] * x + [tex]\frac{36}{13}[/tex]
