SOLUTION: Write an equation of the line that has each pair of intercepts: X-intercept:1, Y-intercept:2

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Question 175485: Write an equation of the line that has each pair of intercepts:
X-intercept:1, Y-intercept:2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
X-intercept:1 means that the point (1,0) is on the line

Y-intercept:2 means that the point (0,2) is on the line


So let's find the equation of the line through the points (1,0) and (0,2)


First let's find the slope of the line through the points and


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%282-0%29%2F%280-1%29 Plug in y%5B2%5D=2, y%5B1%5D=0, x%5B2%5D=0, and x%5B1%5D=1


m=%282%29%2F%280-1%29 Subtract 0 from 2 to get 2


m=%282%29%2F%28-1%29 Subtract 1 from 0 to get -1


m=-2 Reduce


So the slope of the line that goes through the points and is m=-2


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=-2%28x-1%29 Plug in m=-2, x%5B1%5D=1, and y%5B1%5D=0


y=-2%28x-1%29 Simplify


y=-2x%2B-2%28-1%29 Distribute


y=-2x%2B2 Multiply



So the equation that goes through the points and is y=-2x%2B2


Notice how the graph of y=-2x%2B2 goes through the points and . So this visually verifies our answer.
Graph of y=-2x%2B2 through the points and