ACT Math : How to find the equation of a curve

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : X And Y Intercept

Find the slope of the following line: 6x – 4= 10

Possible Answers:

1.5

–1.5

5/2

–5/2

Correct answer:

1.5

Explanation:

Putting the equation in y = mx + b form we obtain y = 1.5x – 2.5.

The slope is 1.5.

Example Question #2 : X And Y Intercept

Find the equation of the line that has an x-intercept of  and a y-intercept of .

Possible Answers:

None of the other answers

Correct answer:

Explanation:

The equation of a line can be written in the form of  where m is the slope and b is the y-intercept. Fortunately, we are given the y-intercept in the problem statement. Therefore, we know that .

 

Now we just need to find the slope of the line. We can find the slope of a line when we know any two points on that line. Generically, the slop of a line is , or more technically, . The problem statement gives use the two intercepts of the line, which can be written as  and . Plugging these points into the equation for slope, we get .

 

We can now plug in our calculated values into the equation of a line to get .

Example Question #3 : X And Y Intercept

What is the x-intercept of the line in the standard  coordinate plane for the following equation?

 

Possible Answers:

12

3

-24

2

Correct answer:

2

Explanation:

This question is asking us to find the x-intercept. Remember that the y-value is equal to zero at the x-intercept. Substitute zero in for the y-variable in the equation and solve for the x-variable.

Add 2 to both sides of the equation.

Divide both sides of the equation by 6.

The line crosses the x-axis at 2. 

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