SOLUTION: Given: m = (y2 - y1)/x2 - x1), y = mx + b, and the points (-2, 2) and (2, 4). Find the y-intercept. Write the equation of the line in slope-intercept form

Algebra ->  Linear-equations -> SOLUTION: Given: m = (y2 - y1)/x2 - x1), y = mx + b, and the points (-2, 2) and (2, 4). Find the y-intercept. Write the equation of the line in slope-intercept form      Log On


   

Question 530233: Given: m = (y2 - y1)/x2 - x1), y = mx + b, and the points (-2, 2) and (2, 4).
Find the y-intercept. Write the equation of the line in slope-intercept form
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=-2 and y%5B1%5D=2.
Also, is the second point . So this means that x%5B2%5D=2 and y%5B2%5D=4.


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


m=%284-2%29%2F%282--2%29 Plug in y%5B2%5D=4, y%5B1%5D=2, x%5B2%5D=2, and x%5B1%5D=-2


m=%282%29%2F%282--2%29 Subtract 2 from 4 to get 2


m=%282%29%2F%284%29 Subtract -2 from 2 to get 4


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--2%29 Plug in m=1%2F2, x%5B1%5D=-2, and y%5B1%5D=2


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


y-2=%281%2F2%29x%2B%281%2F2%29%282%29 Distribute


y-2=%281%2F2%29x%2B1 Multiply


y=%281%2F2%29x%2B1%2B2 Add 2 to both sides.


y=%281%2F2%29x%2B3 Combine like terms.


So the equation that goes through the points and is y=%281%2F2%29x%2B3


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Jim