### All ACT Math Resources

## Example Questions

### Example Question #1 : X And Y Intercept

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

**Possible Answers:**

1.5

–1.5

5/2

–5/2

**Correct answer:**

1.5

Putting the equation in *y* = *mx* + *b* form we obtain *y* = 1.5*x* – 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:**

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

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.

### All ACT Math Resources

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