Answer:
2 possible answers: Graph 1 and graph 3, graph 2 and graph 3
Step-by-step explanation:
Perpendicular lines will have opposite reciprocal slopes.
I will start by putting all of the equations into slope-intercept form, so it will be easier to compare the slopes.
y=1/2x+ 4 ~ This is already in slope-intercept form, so it is fine
y-3=1/2(x-6) ~ the original equation
y-3=1/2x-3 ~ I did distributive property on the right side of the equal sign
y=1/2x ~ I added 3 to both sides to get y by itself
6x+3y=18 ~ the original equation
3y=-6x+18 ~ I subtract 6x from both sides to get the y alone on the left side
y=-2x+6 ~ I divided both sides by 3 to get y by itself
4y-8x=6 ~ the original equation
4y=8x+6 ~ I added 8x to both sides to get the y alone on the left side
y=2x+3/2 ~ I divided both sides by 4 to get y by itself (also can be written as y=2x+1 1/2)
Now, you can compare the slopes easier. You'll notice the first and second equation both have the SAME slope, so those are parallel. The third and fourth equations are opposite, but not the reciprocal of each other.
The slope of a line perpendicular to the first graph would be -2.
The slope of a line perpendicular to the second graph would be -2.
The slope of a line perpendicular to the third graph would be 1/2.
The slope of a line perpendicular to the fourth graph would be -1/2.
Therefore, the first graph would be perpendicular to the third graph. The second graph would be perpendicular to the third graph. The third graph would be perpendicular to the first and second graphs. The fourth graph is not perpendicular to any of these graphs.
