Answer:
(0, -12)
Step-by-step explanation:
In order to find the y-intercept of the equation y = mx + b ( where m is the slope and b is the y-intercept), we first have to find the slope. We can do this by using the two points given to us.
To find the slope:
The slope is equal to: [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Let's plug (5,8) and (12,36) into the equation:
[tex]\frac{36 - 8}{12 - 5}[/tex]
Now let's solve for the slope:
36 -8 = 28
12 - 5 = 7
So we get: [tex]\frac{28}{7}[/tex]
Now that we've found the value of the slope, we can put it into the equation:
y = [tex]\frac{28}{7}[/tex]x + b
To find the value of b, we can input the values of one of the given points into the equation and solve for b. Let's use (5,8):
Input the values of x and y into the equation: 8 = [tex]\frac{28}{7}[/tex](5) + b
Multiple [tex]\frac{28}{7}[/tex] by 5: 8 = [tex]\frac{140}{7}[/tex] + b
Divide 140 by 7: 8 = 20 + b
Subtract 20 from both sides of the equation to isolate b:
8 - 20 = 20 - 20 + b
-12 = b
The y-intercept is (0, -12).
