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 : How To Find The Equation Of A Curve

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

Possible Answers:

–5/2

–1.5

5/2

1.5

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 : How To Find The Equation Of A Curve

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

 

Possible Answers:

3

2

-24

12

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. 

Example Question #3 : How To Find The Equation Of A Curve

What is the equation of a line that has an x-intercept of 4 and a y-intercept of -6?

Possible Answers:

Correct answer:

Explanation:

The equation of a line can be written in the following form:

 

In this formula, is the slope, and b represents the y-intercept. The problem provides the y-intercept; therefore, we know the following information:

We can calculate the slope of the line, because if any two points on the function are known, then the slope can be calculated. Generically, the slope of a line is defined as the function's rise over run, or more technically, the changes in the y-values over the changes in the x-values.  It is formally written as the following equation:

The problem provides the two intercepts of the line, which can be written as  and . Substitute these points into the equation for slope and solve: 

.

Substitute the calculated values into the general equation of a line to get the correct answer: 

.

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