Test Review: Understanding Slope and Intercepts

• Slope: 3, y-intercept: 5

• Slope: 5, y-intercept: 3

• Slope: -3, y-intercept: -5

• Slope: 5, y-intercept: -3

Answer explanation

In the equation y = 3x + 5, the slope is the coefficient of x, which is 3, and the y-intercept is the constant term, which is 5. Therefore, the correct choice is Slope: 3, y-intercept: 5.

Tags

CCSS.HSS.ID.C.7

Answer explanation

To convert to slope-intercept form (y = mx + b), isolate y: 2x - 4y = 8 becomes -4y = -2x + 8, then y = \frac{1}{2}x - 2. Thus, the correct answer is y = \frac{1}{2}x - 2.

Tags

CCSS.HSA.CED.A.4

Calculate the slope of the line passing through the points (2, 3) and (4, 7).

• 2

• 4

Answer explanation

To find the slope (m) between points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (7 - 3) / (4 - 2) = 4 / 2 = 2. Thus, the slope is 2.

Tags

CCSS.HSS.ID.C.7

• The line rises 3 units for every 1 unit it moves to the right.

• The line falls 3 units for every 1 unit it moves to the right.

• The line rises 4 units for every 1 unit it moves to the right.

• The line falls 4 units for every 1 unit it moves to the right.

Answer explanation

The slope of the line, -3, indicates that for every 1 unit the line moves to the right, it falls 3 units. Therefore, the correct interpretation is that the line falls 3 units for every 1 unit it moves to the right.

Tags

CCSS.HSS.ID.C.7

Answer explanation

The equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Here, the slope is -\frac{2}{3} and the y-intercept is 6, making the correct choice: Slope: -\frac{2}{3}, y-intercept: 6.

Tags

CCSS.HSS.ID.C.7

Answer explanation

To convert to slope-intercept form, isolate y: 3y = 6x - 9, then y = 2x - 3. The correct answer is y = 2x - 3.

Tags

CCSS.HSA.CED.A.4

CCSS.HSA.REI.B.3

Calculate the slope of the line passing through the points (-1, -2) and (3, 4).

• 2

Answer explanation

To find the slope (m) between points (-1, -2) and (3, 4), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (4 - (-2)) / (3 - (-1)) = 6 / 4 = 3/2. However, the correct answer is 2, indicating a possible error in the options.

• The line crosses the y-axis at (0, 5).

• The line crosses the y-axis at (0, -7).

• The line crosses the y-axis at (5, 0).

• The line crosses the y-axis at (-7, 0).

Answer explanation

The y-intercept of a line is the point where it crosses the y-axis, which occurs when x = 0. In the equation y = 5x - 7, substituting x = 0 gives y = -7. Thus, the line crosses the y-axis at (0, -7).

Tags

CCSS.HSS.ID.C.7

CCSS.HSF.IF.B.4

CCSS.HSF.LE.B.5

Answer explanation

The equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Here, the slope is \frac{4}{5} and the y-intercept is -1, making the correct choice: Slope: \frac{4}{5}, y-intercept: -1.

Tags

CCSS.HSS.ID.C.7

Answer explanation

To convert to slope-intercept form (y = mx + b), isolate y: 2y = -5x + 10, then y = -\frac{5}{2}x + 5. The correct choice is y = -\frac{5}{2}x + 5.

Tags

CCSS.HSA.CED.A.4