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.
Since the new line is parallel to 5x + 2y - 8 = 0 , it must be
5x - 2y = c , that is, differing only in the constant
the y-intercept of the other line is (0,3), by mentally letting x = 0
sub in that point
5(0) + 2(3) = c , c = 6
new equation: 5x + 2y = 6 or 5x + 2y - 6 = 0
To find the equation of a line that is parallel to another line, we need to determine the slope of the given line. The general form of a line equation is y = mx + b, where m is the slope and b is the y-intercept.
First, let's rearrange the equation 5x + 2y - 8 = 0 into y = mx + b form:
2y = -5x + 8
y = (-5/2)x + 4
From this equation, we can see that the slope of the given line is -5/2.
Since the line we are looking for is parallel to this line, it will have the same slope of -5/2.
Next, we need to find the y-intercept of the second line x + 4y - 12 = 0.
Rearrange the equation x + 4y - 12 = 0 into y = mx + b form:
4y = -x + 12
y = (-1/4)x + 3
From this equation, we can see that the y-intercept of the second line is 3.
Now we have the slope (-5/2) and the y-intercept (3) of the line we are looking for.
Using the slope-intercept form y = mx + b, substitute the slope and y-intercept values into the equation:
y = (-5/2)x + 3
Therefore, the equation for the line that is parallel to the line 5x + 2y - 8 = 0 and has the same y-intercept as x + 4y - 12 = 0 is y = (-5/2)x + 3.