Slope and Intercept Practice Questions

To review these concepts, go to Slope and Intercept Study Guide.

Slope and Intercept Practice Questions

Problems

Practice 1

For each equation, find the slope and the y-intercept.

1. y = 9x + 4
2. 
3. y = –5x
4. y = 12
5. y = x

Practice 2

For each equation, find the slope and the y-intercept.

1. y –3 = x + 4
2. 5y = –15x –25
3. y = 7(x + 1)
4. x + y= 0
5. x = 4y –24

Practice 3

Write the equation of a line that is parallel to each of the following equations, and write the equation of a line that is perpendicular to each equation.

1. y = 2x – 9
2. y = –7x
3. 
4. 
5. y = x

Solutions

Practice 1

1. The equation y = 9x + 4 is in slope-intercept form, because y is alone on one side of the equation, and the other side of the equation contains no more than two terms, with x appearing in no more than one of those terms. The slope is the coefficient of x, so the slope of this line is 9. The y-intercept is the constant in the equation, which is 4.
2. The equation y = x – 6 is in slope-intercept form. The slope of the line is the coefficient of x, , and the y-intercept of the line is the constant in the equation, –6.
3. The equation y = –5x is in slope-intercept form. The slope of the line is the coefficient of x, –5. There is no constant in this equation, so the y-intercept of the line is 0.
4. The equation y = 12 is in slope-intercept form. There is no x term in the equation, so the slope of the line is 0. The y-intercept of the line is the constant in the equation, 12.
5. The equation y = x is in slope-intercept form. The slope of the line is the coefficient of x, 1. There is no constant in this equation, so the y-intercept of the line is 0.

Practice 2

1. The equation y – 3 = x + 4 is not in slope-intercept form, because y is not alone on one side of the equation. Because 3 is subtracted from y, we must use the opposite operation, addition, to remove –3 from the left side of the equation. Add 3 to both sides of the equation:

   y – 3 + 3 = x + 4 + 3

   y = x + 7

   The equation is now in slope-intercept form. The slope is the coefficient of x, so the slope of this line is 1. The y-intercept is the constant in the equation, which is 7.

2. The equation 5y = –15x – 25 is not in slope-intercept form, because y is not alone on one side of the equation. Because y is multiplied by 5, we must divide both sides of the equation by 5:

   

   y = –3x – 5

   The equation is now in slope-intercept form. The slope is the coefficient of x, so the slope of this line is –3. The y-intercept is the constant in the equation, which is –5.

3. The equation y = 7(x + 1) is not in slope-intercept form. Although y is alone on one side of the equation, there are parentheses around two terms on the right side. Use the distributive law to simplify the right side of the equation. Multiply x and 1 by 7:

   7(x + 1) = 7x + 7

   The equation is now in slope-intercept form:

   y = 7x + 7

   The slope is the coefficient of x, so the slope of this line is 7. The y-intercept is the constant in the equation, which is 7.

4. The equation x + y = 0 is not in slope-intercept form, because y is not alone on one side of the equation. Because x is added to y, we must use the opposite operation, subtraction, to remove x from the left side of the equation. Subtract x from both sides of the equation:

   x – x + y = 0 – x

   y = –x

   The equation is now in slope-intercept form. The slope is the coefficient of x, so the slope of this line is –1. There is no constant in this equation, so the y-intercept of the line is 0.

5. The equation x = 4y – 24 is not in slope-intercept form, because y is not alone on one side of the equation. In the equation, y is multiplied by 4, and then 24 is subtracted from that term. First, add 24 to both sides of the equation:

   x + 24 = 4y – 24 + 24

   x + 24 = 4y

   Because y is multiplied by 4, divide both sides of the equation by 4:

   

   y = x + 6

   The equation is now in slope-intercept form. The slope is the coefficient of x, so the slope of this line is . The y-intercept is the constant in the equation, which is 6.

Practice 3

1. The slope of the line y = 2x – 9 is 2, because the line is in slope-intercept form, and the coefficient of x is 2. Any line with a slope of 2, such as y = 2x + 1, is parallel to the line y = 2x – 9.

   Because the slope of the line y = 2x – 9 is 2, lines that are perpendicular to this line will have slopes that are the negative reciprocal of 2. To find the negative reciprocal of 2, divide 1 by 2, and change the sign from positive to negative. The negative reciprocal of 2 is . Any line with a slope of , such as y = x + 1, is perpendicular to the line y = 2x – 9.

    

2. The slope of the line y = –7x is –7, because the line is in slope-intercept form, and the coefficient of x is –7. Any line with a slope of –7, such as y = –7x + 1, is parallel to the line y = –7x.

   Because the slope of the line y = –7x is –7, lines that are perpendicular to this line will have slopes that are the negative reciprocal of –7. To find the negative reciprocal of –7, divide 1 by –7, and change the sign from negative to positive. The negative reciprocal of –7 is . Any line with a slope of , such as y = x + 1, is perpendicular to the line y = –7x.

3. The slope of the line y = is , because the line is in slope-intercept form, and the coefficient of x is . Any line with a slope of , such as y = , is parallel to the line y =

   Because the slope of the line y = is , lines that are perpendicular to this line will have slopes that are the negative reciprocal of . To find the negative reciprocal of , switch the numerator and the denominator of the fraction, and change the sign from positive to negative. The negative reciprocal of is . Any line with a slope of , such as y = –, is perpendicular to the line y = .

4. The slope of the line + 34 is , because the line is in slope-intercept form, and the coefficient of x is . Any line with a slope of , such as y = + 1, is parallel to the line + 34.

   Because the slope of the line + 34 is , lines that are perpendicular to this line will have slopes that are the negative reciprocal of . To find the negative reciprocal of , switch the numerator and the denominator of the fraction, and change the sign from negative to positive. The negative reciprocal of is , or 4. Any line with a slope of 4, such as y = 4x + 1, is perpendicular to the line + 34.

5. The slope of the line y = x is 1, because the line is in slope-intercept form, and the coefficient of x is 1. Any line with a slope of 1, such as y = x + 1, is parallel to the line y = x.

   Because the slope of the line y = x is 1, lines that are perpendicular to this line will have slopes that are the negative reciprocal of 1. To find the negative reciprocal of 1, divide 1 by 1, and change the sign from positive to negative. Because 1 divided by 1 is 1, the negative reciprocal of 1 is –1. Any line with a slope of –1, such as y = –x + 1, is perpendicular to the line y = x.