SOLUTION: how do u find the equation of a line when given the y intercept and a point? grade 9 level eg: given y intercept as 3 and point as (-6,7)

Algebra ->  Linear-equations -> SOLUTION: how do u find the equation of a line when given the y intercept and a point? grade 9 level eg: given y intercept as 3 and point as (-6,7)      Log On


   

Question 594498: how do u find the equation of a line when given the y intercept and a point? grade 9 level eg: given y intercept as 3 and point as (-6,7)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the y-intercept is 3, then this means that the line goes through (0,3)

So the line goes through the points (0,3) and (-6,7)


Now let's find the equation of the line that goes through the points (0,3) and (-6,7)


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=0 and y%5B1%5D=3.
Also, is the second point . So this means that x%5B2%5D=-6 and y%5B2%5D=7.


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


m=%287-3%29%2F%28-6-0%29 Plug in y%5B2%5D=7, y%5B1%5D=3, x%5B2%5D=-6, and x%5B1%5D=0


m=%284%29%2F%28-6-0%29 Subtract 3 from 7 to get 4


m=%284%29%2F%28-6%29 Subtract 0 from -6 to get -6


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-3=%28-2%2F3%29%28x-0%29 Plug in m=-2%2F3, x%5B1%5D=0, and y%5B1%5D=3


y-3=%28-2%2F3%29x%2B%28-2%2F3%29%28-0%29 Distribute


y-3=%28-2%2F3%29x%2B0 Multiply


y=%28-2%2F3%29x%2B0%2B3 Add 3 to both sides.


y=%28-2%2F3%29x%2B3 Combine like terms.


So the equation that goes through the points and is y=%28-2%2F3%29x%2B3