find an equation for the line that passes through the point (2,-5) and
a) is parallel to the x-axis
b) is parallel to the y-axis
c) is parallel to the line 2x-4y=3
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parallel to the x-axis ---> horizontal line of slope=0
parallel to the y-axis ---> vertical line of undefined slope
parallel lines have same slope
y=(1/2)x -3/4 ------> slope=1/2
y+5 = (1/2)x -1
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b) y = -5 parallel to x-axis means y is constant, since we have (2,-5) on the line
y = -5 is the line
c) x = 2
parallel to y-axis means x is constant, since we have (2,-5) on the line x = 2 is the line
d) 2x - 4y = 3
4y = 2x - 3
y = 1/2x - 3/4
You see the slope is 1/2 i.e m
For our line y = mx + b to be parallel to y = 1/2x - 3/4 both should have the same slope i.e 1/2
y = 1/2x + b
Substitute x = 2 and y =-5
-5 = 1/2 * 2 + b
-5 = 1 + b
b = -6
So our line is y = 1/2x - 6