Slope & COP Test

Which equation finds the slope from two points?

Answer explanation

The correct equation to find the slope (m) from two points (x1, y1) and (x2, y2) is m=(y2-y1)/(x2-x1). This formula calculates the change in y over the change in x, which defines the slope of the line between the two points.

Tags

CCSS.8.EE.B.5

Which of the following is the slope-intercept form?

• y = mx + b

• y = m + bx

• y = mx - b

• y = b + mx

Answer explanation

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept. This matches the first option, making it the correct choice.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

In y = kx, what does k represent?

• k is the y-intercept

• k is the x-intercept

• k is the value of y when x is zero.

• k is the constant of proportionality.

Answer explanation

In the equation y = kx, k represents the constant of proportionality, indicating how y changes with respect to x. It defines the ratio of y to x, making it the correct choice.

Tags

CCSS.HSF-LE.A.1B

In y = 5x, what is the constant of proportionality?

• y

• 5x

• 0

• 5

Answer explanation

In the equation y = 5x, the constant of proportionality is the coefficient of x, which is 5. This means y varies directly with x, and for every unit increase in x, y increases by 5.

Tags

CCSS.7.RP.A.2B

Which math term describes how steep a line is?

• slope

• intercept

• coordinate

• angle

Answer explanation

The term that describes how steep a line is in mathematics is 'slope'. It quantifies the angle of inclination of the line, indicating how much it rises or falls as you move along the x-axis.

Tags

CCSS.8.EE.B.5

What is the constant of proportionality in the table?

• $3

• $4

• $2

• $9

Answer explanation

The constant of proportionality is found by dividing the dependent variable by the independent variable. In this case, the ratio that consistently equals 9 indicates that $9 is the correct constant of proportionality.

Tags

CCSS.7.RP.A.2B

Is this graph proportional or non proportional?

• proportional

• non proportional

Answer explanation

The graph is non-proportional because the relationship between the variables does not maintain a constant ratio. In a proportional graph, the line would pass through the origin and have a consistent slope.

Tags

CCSS.7.RP.A.2D

Is the relationship in this table proportional?

• Yes

• No

Answer explanation

The relationship is not proportional because the ratios of corresponding values do not remain constant. Therefore, the correct answer is 'No'.

Tags

CCSS.7.RP.A.2B

Is the relationship in the graph proportional?

• Yes

• No

Answer explanation

Yes, the relationship in the graph is proportional because it shows a constant ratio between the two variables, indicating that as one variable increases, the other increases at a consistent rate.

Tags

CCSS.7.RP.A.2D

Find the slope between the points (-2, 7) and (3, 8).

Answer explanation

To find the slope, use the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Here, \( (x_1, y_1) = (-2, 7) \) and \( (x_2, y_2) = (3, 8) \). Thus, \( m = \frac{8 - 7}{3 - (-2)} = \frac{1}{5} \). The correct answer is \( \frac{1}{5} \).

Tags

CCSS.8.EE.B.5