Answer:
First let's find the slope of the line through the points and
Note: is the first point . So this means that x%5B1%5D=-2 and y%5B1%5D=0.
Also, is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=3.
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.
m=%283-0%29%2F%280--2%29 Plug in y%5B2%5D=3, y%5B1%5D=0, x%5B2%5D=0, and x%5B1%5D=-2
m=%283%29%2F%280--2%29 Subtract 0 from 3 to get 3
m=%283%29%2F%282%29 Subtract -2 from 0 to get 2
So the slope of the line that goes through the points and is m=3%2F2
Now let's use the point slope formula:
y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula
y-0=%283%2F2%29%28x--2%29 Plug in m=3%2F2, x%5B1%5D=-2, and y%5B1%5D=0
y-0=%283%2F2%29%28x%2B2%29 Rewrite x--2 as x%2B2
y-0=%283%2F2%29x%2B%283%2F2%29%282%29 Distribute
y-0=%283%2F2%29x%2B3 Multiply
y=%283%2F2%29x%2B3 Simplify
So the equation that goes through the points and is y=%283%2F2%29x%2B3
Notice how the graph of y=%283%2F2%29x%2B3 goes through the points and . So this visually verifies our answer.
Graph of y=%283%2F2%29x%2B3 through the points and
Step-by-step explanation:
