SOLUTION: A line passes though the points(-10,-4) and(-1,2). What is the y-intercept of the intercept line?

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Question 884888: A line passes though the points(-10,-4) and(-1,2). What is the y-intercept of the intercept line?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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=-10 and y%5B1%5D=-4.
Also, is the second point . So this means that x%5B2%5D=-1 and y%5B2%5D=2.


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


m=%282--4%29%2F%28-1--10%29 Plug in y%5B2%5D=2, y%5B1%5D=-4, x%5B2%5D=-1, and x%5B1%5D=-10


m=%286%29%2F%28-1--10%29 Subtract -4 from 2 to get 6


m=%286%29%2F%289%29 Subtract -10 from -1 to get 9


m=2%2F3 Reduce


So the slope of the line that goes through the points and is m=2%2F3


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--4=%282%2F3%29%28x--10%29 Plug in m=2%2F3, x%5B1%5D=-10, and y%5B1%5D=-4


y--4=%282%2F3%29%28x%2B10%29 Rewrite x--10 as x%2B10


y%2B4=%282%2F3%29%28x%2B10%29 Rewrite y--4 as y%2B4


y%2B4=%282%2F3%29x%2B%282%2F3%29%2810%29 Distribute


y%2B4=%282%2F3%29x%2B20%2F3 Multiply


y=%282%2F3%29x%2B20%2F3-4 Subtract 4 from both sides.


y=%282%2F3%29x%2B8%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%282%2F3%29x%2B8%2F3


and we can see that the y-intercept is (0, 8/3)