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 #1 : How To Find The Equation Of A Curve

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 #2 : How To Find The Equation Of A Curve

Given that  is a line, at what  point does the line cross the ?

Possible Answers:

Correct answer:

Explanation:

The question is asking you to find the x-intercept. Remember that at the x-intercept, .

Plug in that value for y and solve:

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