ACT Math : ACT Math
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Example Questions
Example Question #2 : How To Find Out If Lines Are Perpendicular
Line 
Yes, because the product of their slopes is not 
No, because the product of their slopes is
No, because the product of their slope is not 
Yes, because the product of their slopes is 
Yes, because the product of their slopes is
The product of perpendicular slopes is always 
Since line 
Since the two slopes' product is 
Example Question #3 : How To Find Out If Lines Are Perpendicular
Are the following two lines perpendicular:
For two lines to be perpendicular they have to have slopes that multiply to get 
For the first line, 
Example Question #2 : How To Find Out If Lines Are Perpendicular
Which of the following equations represents a line that is perpendicular to the line with points 
If lines are perpendicular, then their slopes will be negative reciprocals.
First, we need to find the slope of the given line.
Because we know that our given line's slope is 
Example Question #711 : Act Math
Consider the lines described by the following two equations:
4y = 3x2
3y = 4x2
Find the vertical distance between the two lines at the points where x = 6.
48
12
36
21
44
21
Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:
Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.
Example Question #712 : Act Math
For the line
Which one of these coordinates can be found on the line?
(9, 5)
(6, 5)
(6, –12)
(3, 7)
(3, –6)
(3, –6)
To test the coordinates, plug the x-coordinate into the line equation and solve for y.
y = 1/3x -7
Test (3,-6)
y = 1/3(3) – 7 = 1 – 7 = -6 YES!
Test (3,7)
y = 1/3(3) – 7 = 1 – 7 = -6 NO
Test (6,-12)
y = 1/3(6) – 7 = 2 – 7 = -5 NO
Test (6,5)
y = 1/3(6) – 7 = 2 – 7 = -5 NO
Test (9,5)
y = 1/3(9) – 7 = 3 – 7 = -4 NO
Example Question #713 : Act Math
Solve the following system of equations:
–2x + 3y = 10
2x + 5y = 6
(3, 5)
(–2, 2)
(2, 2)
(–2, –2)
(3, –2)
(–2, 2)
Since we have –2x and +2x in the equations, it makes sense to add the equations together to give 8y = 16 yielding y = 2. Then we substitute y = 2 into one of the original equations to get x = –2. So the solution to the system of equations is (–2, 2)
Example Question #714 : Act Math
Which of the following sets of coordinates are on the line 
Because this equation is true, the point must lie on the line. The other given answer choices do not result in true equalities.
Example Question #715 : Act Math
Which of the following points can be found on the line 
We are looking for an ordered pair that makes the given equation true. To solve, plug in the various answer choices to find the true equality.
Because this equality is true, we can conclude that the point 
Example Question #1 : How To Find Out If A Point Is On A Line With An Equation
Which of the following points is on the line 
The only thing that is necessary to solve this question is to see if a given 
Example Question #716 : Act Math
What is the slope of line 3 = 8y - 4x?
-2
0.5
2
-0.5
0.5
Solve equation for y. y=mx+b, where m is the slope
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