### All SAT Math Resources

## Example Questions

### Example Question #596 : Geometry

Find the x-intercepts of .

**Possible Answers:**

**Correct answer:**

To find the x-intercepts, plug into the equation and solve for .

Don't forget that there are two solutions, both negative and positive!

### Example Question #597 : Geometry

A line with the exquation passes through the point . What is the -intercept?

**Possible Answers:**

**Correct answer:**

By plugging in the coordinate, we can figure out that . The -Intercept is when , plugging in 0 for gives us .

### Example Question #598 : Geometry

What are the -intercept(s) of the following line:

**Possible Answers:**

**Correct answer:**

We can factor and set equal to zero to determine the -intercepts.

satisfies this equation.

Therefore our -intercepts are and .

### Example Question #599 : Geometry

Which of the following lines does not intersect the line ?

**Possible Answers:**

**Correct answer:**

Parallel lines never intersect, so you are looking for a line that has the same slope as the one given. The slope of the given line is –4, and the slope of the line in *y* = –4*x* + 5 is –4 as well. Since these two lines have equal slopes, they will run parallel and can never intersect.

### Example Question #600 : Geometry

Find the y-intercept of .

**Possible Answers:**

3

5

7

12

14

**Correct answer:**

7

To find the y-intercept, set x equal to zero and solve for y.

This gives y = 3(0)^{2} + 2(0) +7 = 7.

### Example Question #601 : Geometry

The slope of a line is . The line passes through . What is the x-intercept?

**Possible Answers:**

None of the available answers

**Correct answer:**

The equation for a line is:

, or in this case

We can solve for by plugging in the values given

Our line is now

Our x-intercept occurs when , so plugging in and solving for :

### Example Question #602 : Geometry

Determine the x-intercept for the equation:

**Possible Answers:**

**Correct answer:**

The x-intercept is the x-value when the value of . Substitute this value and solve for .

The x-intercept is .

### Example Question #603 : Geometry

What is the y intercept of

**Possible Answers:**

y=12

y=3

The line does not cross the y axis.

y=-3

**Correct answer:**

y=3

To find the y intercept, substitute x=0

### Example Question #604 : Geometry

At what point does the line intersect the y-axis?

**Possible Answers:**

None of the given answers

**Correct answer:**

We know that in slope-intercept form, , that represents the y-intercept. So, let's rewrite this line and put it in slope-intercept form.

Therefore, when , . With this in mind, our y-intercept is .

### Example Question #605 : Geometry

Give the area of the triangle on the coordinate plane that is bounded by the -axis, and the lines of the equations and .

**Possible Answers:**

None of the other choices gives the correct response.

**Correct answer:**

It is necessary to find the vertices of the triangle, which can be done by finding the three points at which two of the three lines intersect.

The intersection of the -axis - the line - and the line of the equation , is found by noting that if , then, by substitution, ; this point of intersection is at , the origin.

The intersection of the -axis and the line of the equation is the -intercept of the latter line. Since its equation is written in slope-intercept form , with the -coordinate of the -intercept, this intercept is .

The intersection of the lines with equations and can be found using the substitution method, setting in the latter equation and solving for :

Since , , making the point of intersection.

The lines in question are graphed below, and the triangle they bound is shaded:

If we take the vertical side as the base, its length is seen to be 3; the height is the horizontal distance to the opposite vertex, which is its -coordinate . The area is half the product of the two, or

.

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