Question 186063This question is from textbook 9780136028956
: Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through (2,4) and has the same y-intercept as the line whose equation is x - 4y = 8
This question is from textbook 9780136028956
Answer by hkelson(7)   (Show Source):
You can put this solution on YOUR website! I can understand how this may confuse you. Hopefully this will simplify it a little more.
You know the slope-intercept form of an equation is y=mx+b.
The line has to pass through the point (2,4) and has the same y-intercept as a line that passes through x-4y=8.
So you first solve the equation for y in order to get it into slope-intercept form.
x-4y = 8 : Subtract x from both sides
-4y= -x+8 : Divide both sides by -4 to get y by itself.
y= 1/4x-8/4 : Simplify it
y= 1/4x-2
Now that it is in slope intercept form you know that the y-intercept is -2.
You still have to figure out what the slope of the new line will be.
Plug the coordinates in (2,4) as x and y into the equation and leave out the 1/4 since you are solving for a new slope.
y= mx-2
4= m(2)-2 : Add 2 to both sides
6= m(2) : Divide both sides by 2
3= m
So the equation for your new line that passes through (2,4) and has the y-intercept as the line that passes through x-4y = 8 is:
y= 3x-2
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