SOLUTION: Use the given conditions to write an equation for the line in slope-intercept form. Passing through (-6, -2) and (-8, -3)

Algebra ->  Equations -> SOLUTION: Use the given conditions to write an equation for the line in slope-intercept form. Passing through (-6, -2) and (-8, -3)      Log On


   

Question 644375: Use the given conditions to write an equation for the line in slope-intercept form.
Passing through (-6, -2) and (-8, -3)
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=-6 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=-8 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=%28-3--2%29%2F%28-8--6%29 Plug in y%5B2%5D=-3, y%5B1%5D=-2, x%5B2%5D=-8, and x%5B1%5D=-6


m=%28-1%29%2F%28-8--6%29 Subtract -2 from -3 to get -1


m=%28-1%29%2F%28-2%29 Subtract -6 from -8 to get -2


m=1%2F2 Reduce


So the slope of the line that goes through the points and is m=1%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--2=%281%2F2%29%28x--6%29 Plug in m=1%2F2, x%5B1%5D=-6, and y%5B1%5D=-2


y--2=%281%2F2%29%28x%2B6%29 Rewrite x--6 as x%2B6


y%2B2=%281%2F2%29%28x%2B6%29 Rewrite y--2 as y%2B2


y%2B2=%281%2F2%29x%2B%281%2F2%29%286%29 Distribute


y%2B2=%281%2F2%29x%2B3 Multiply


y=%281%2F2%29x%2B3-2 Subtract 2 from both sides.


y=%281%2F2%29x%2B1 Combine like terms.


So the equation that goes through the points and is y=%281%2F2%29x%2B1


Notice how the graph of y=%281%2F2%29x%2B1 goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F2%29x%2B1 through the points and