ACT Math : Other Lines
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Example Questions
Example Question #81 : Lines
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
44
12
21
36
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 #2 : How To Find Out If A Point Is On A Line With An Equation
For the line
Which one of these coordinates can be found on the line?
(3, –6)
(9, 5)
(6, 5)
(3, 7)
(6, –12)
(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 #3 : How To Find Out If A Point Is On A Line With An Equation
Solve the following system of equations:
–2x + 3y = 10
2x + 5y = 6
(3, –2)
(–2, –2)
(–2, 2)
(2, 2)
(3, 5)
(–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 #3 : How To Find Out If A Point Is On A Line With An Equation
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 #2 : Other Lines
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 #1 : Other Lines
What is the slope of line 3 = 8y - 4x?
-2
0.5
-0.5
2
0.5
Solve equation for y. y=mx+b, where m is the slope
Example Question #4 : How To Find The Slope Of A Line
If 2x – 4y = 10, what is the slope of the line?
–0.5
–5/2
2
0.5
–2
0.5
First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.
Example Question #1 : How To Find Slope Of A Line
What is the slope of the line with equation 4x – 16y = 24?
1/8
1/2
–1/4
1/4
–1/8
1/4
The equation of a line is:
y = mx + b, where m is the slope
4x – 16y = 24
–16y = –4x + 24
y = (–4x)/(–16) + 24/(–16)
y = (1/4)x – 1.5
Slope = 1/4
Example Question #31 : Other Lines
What is the slope of a line which passes through coordinates 
Slope is found by dividing the difference in the 
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