A line is parallel to 5x+2y-8=0 and has the same y-intercept as x+4y-12=0
Find an equation for the line.
first make each into y=mx+b by rearranging
5x+2y-8=0
2y=-5x+8
y=-5/2x +4
and
x+4y-12=0
4y=-x+12
y=-1/4x+3
because the line is parallel to the first equation it will have the same value for the slope (m)
y=-5/2x+b
now use the second equation to solve for the value of y at the y intercept (i.e. we know x is zero, solve y)
y=-1/4x+3
y=-1/4(0)+3
y=3
so the y intercept of our new equation is (x,y)=(0,3)
put this into our new equation to solve for b
y=-5/2x+b
3=-5/2(0)+b
3=b
so our new equation is
y=-5/2x+3
To find the equation of a line parallel to a given line, we need two pieces of information: the slope of the given line and the y-intercept of the new line.
Let's first find the slope of the given line 5x + 2y - 8 = 0. Rearranging this equation in slope-intercept form (y = mx + b), we get:
2y = -5x + 8
y = (-5/2)x + 4
From this equation, we can see that the slope of the given line is -5/2.
Now, let's find the y-intercept of the new line by considering the equation x + 4y - 12 = 0. Rearranging this equation in slope-intercept form, we get:
4y = -x + 12
y = (-1/4)x + 3
From this equation, we can see that the y-intercept of the new line is 3.
Now that we have the slope (-5/2) and the y-intercept (3) for the new line, we can write its equation in slope-intercept form (y = mx + b):
y = (-5/2)x + 3
Therefore, the equation for the line that is parallel to 5x + 2y - 8 = 0 and has the same y-intercept as x + 4y - 12 = 0 is y = (-5/2)x + 3.