Slope Intercept Before And After Quiz

1) What is the slope in the following equation?
y = 4x - 4

put your answer as one number

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). In the given equation, y = 4x - 4, the coefficient of x is 4, which indicates that for every increase of 1 in x, y increases by 4. Therefore, the slope of this equation is 4.

Explanation

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). In the given equation, y = 4x - 4, the coefficient of x is 4, which indicates that for every increase of 1 in x, y increases by 4. Therefore, the slope of this equation is 4.

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2) What is the y-interecept of the following equation?
y = 3x - 2

put your answer as just a number

The y-intercept of an equation represents the point where the line intersects the y-axis. In the given equation, y = 3x - 2, the y-intercept is represented by the constant term, which is -2. Therefore, the y-intercept of the equation is -2.

Explanation

The y-intercept of an equation represents the point where the line intersects the y-axis. In the given equation, y = 3x - 2, the y-intercept is represented by the constant term, which is -2. Therefore, the y-intercept of the equation is -2.

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3) What is the slope and y intercept of the following equaiton?

y = -5x + 4

write your first number, then a comma, and your second number

The slope of the equation y = -5x + 4 is -5, which represents the rate at which the line is decreasing or increasing. The y-intercept is 4, which is the point where the line crosses the y-axis.

Explanation

The slope of the equation y = -5x + 4 is -5, which represents the rate at which the line is decreasing or increasing. The y-intercept is 4, which is the point where the line crosses the y-axis.

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5) What is the linear equation in slope intercept form (y = mx + b; where m is the slope and b is the y intercept)

The given correct answer for this question is y = -7x - 4. This equation is in slope-intercept form, y = mx + b, where m is the slope (-7 in this case) and b is the y-intercept (-4 in this case).

Explanation

The given correct answer for this question is y = -7x - 4. This equation is in slope-intercept form, y = mx + b, where m is the slope (-7 in this case) and b is the y-intercept (-4 in this case).

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6) What is the linear equation of this line?

Y = 8x + 1

Y = 1/8x + 1

Y = -1/8x + 1

The correct answer is y = 1/8x + 1. This equation represents a line with a slope of 1/8 and a y-intercept of 1. The slope of 1/8 means that for every 1 unit increase in x, the y-value will increase by 1/8. The y-intercept of 1 indicates that the line crosses the y-axis at the point (0, 1). Therefore, this equation accurately represents the linear relationship between x and y for the given line.

Explanation

The correct answer is y = 1/8x + 1. This equation represents a line with a slope of 1/8 and a y-intercept of 1. The slope of 1/8 means that for every 1 unit increase in x, the y-value will increase by 1/8. The y-intercept of 1 indicates that the line crosses the y-axis at the point (0, 1). Therefore, this equation accurately represents the linear relationship between x and y for the given line.

7) What is the linear equation of the following line?

Y = 1/5x - 2

Y = 5x - 2

Y = -1/5x - 2

The given equation, y = 1/5x - 2, represents a linear equation. It is in the form y = mx + b, where m is the slope (1/5) and b is the y-intercept (-2). Therefore, the correct linear equation for the given line is y = 1/5x - 2.

Explanation

The given equation, y = 1/5x - 2, represents a linear equation. It is in the form y = mx + b, where m is the slope (1/5) and b is the y-intercept (-2). Therefore, the correct linear equation for the given line is y = 1/5x - 2.

8) How would you graph the following equation?

y = -1/2x + 3

Plot (-1, 2); then plot points by going up 3 and right 1

The correct answer suggests plotting the point (0, 3) as the y-intercept, and then moving down 1 and right 2 (or up 1 and left 2) to plot additional points on the graph. This is because the equation y = -1/2x + 3 is in slope-intercept form, where the coefficient of x (-1/2) represents the slope of the line. Moving down 1 and right 2 (or up 1 and left 2) allows us to find other points on the line based on the given slope.

Explanation

The correct answer suggests plotting the point (0, 3) as the y-intercept, and then moving down 1 and right 2 (or up 1 and left 2) to plot additional points on the graph. This is because the equation y = -1/2x + 3 is in slope-intercept form, where the coefficient of x (-1/2) represents the slope of the line. Moving down 1 and right 2 (or up 1 and left 2) allows us to find other points on the line based on the given slope.

9) What is the slope and y intercept of the following line?

M = 2 and y-intercept is (0, 3)

M = 1 and y-intercept is (0, 3)

M = -1 and y-intercept is (0, 3)

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. In this case, the given equation is y = 1x + 3, which simplifies to y = x + 3. Therefore, the slope is 1 and the y-intercept is (0, 3).

Explanation

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. In this case, the given equation is y = 1x + 3, which simplifies to y = x + 3. Therefore, the slope is 1 and the y-intercept is (0, 3).

10) Write a linear equation for a line that has a slope of 5 and a y-intercept of -4

(your answer should look something like this: y = 2x + 3

The correct answer is y = 5x - 4. This equation represents a line with a slope of 5 and a y-intercept of -4. The slope of 5 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 5. The y-intercept of -4 means that the line intersects the y-axis at the point (0, -4).

Explanation

The correct answer is y = 5x - 4. This equation represents a line with a slope of 5 and a y-intercept of -4. The slope of 5 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 5. The y-intercept of -4 means that the line intersects the y-axis at the point (0, -4).

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