SOLUTION: 4. Write the equation of the line passing through each of the given points with the indicated slope. Give your results in slope-intercept form, where possible. (0, -3)

Algebra ->  Graphs -> SOLUTION: 4. Write the equation of the line passing through each of the given points with the indicated slope. Give your results in slope-intercept form, where possible. (0, -3)      Log On


   

Question 125744: 4. Write the equation of the line passing through each of the given points with the indicated slope. Give your results in slope-intercept form, where possible.

(0, -3), m = -2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of -2 which goes through the point (0,-3), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

y--3=%28-2%29%28x-0%29 Plug in m=-2, x%5B1%5D=0, and y%5B1%5D=-3 (these values are given)


y%2B3=%28-2%29%28x-0%29 Rewrite y--3 as y%2B3


y%2B3=-2x%2B%28-2%29%280%29 Distribute -2

y%2B3=-2x%2B0 Multiply -2 and 0 to get 0

y=-2x%2B0-3 Subtract 3 from both sides to isolate y

y=-2x-3 Combine like terms 0 and -3 to get -3
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Answer:


So the equation of the line with a slope of -2 which goes through the point (0,-3) is:

y=-2x-3 which is now in y=mx%2Bb form where the slope is m=-2 and the y-intercept is b=-3

Notice if we graph the equation y=-2x-3 and plot the point (0,-3), we get (note: if you need help with graphing, check out this solver)

Graph of y=-2x-3 through the point (0,-3)
and we can see that the point lies on the line. Since we know the equation has a slope of -2 and goes through the point (0,-3), this verifies our answer.