Unit 2 Study Guide: Linear Equations-Slope

Part A: Linear equations formulas Matching. 1. _____ Ax + By = C 2. _____ y = mx + b 3. _____ (y-y1) = m(x-x1)

• y = mx + b

• Standard Form

• Ax + By = C

• Slope intercept Form

• (y-y1) = m(x-x1)

• Point Slope Form

Which of the following descriptions would represent a line with a positive slope?

• A line going upwards from left to right

• A line going downwards from left to right

• A horizontal line

• A vertical line

Answer explanation

A line with a positive slope rises as it moves from left to right. Therefore, the correct description is 'A line going upwards from left to right', which indicates an increase in value.

Tags

CCSS.8.EE.B.6

Which of the following descriptions would represent a line with a negative slope?

• A line slanting upwards from left to right

• A line slanting downwards from left to right

• A horizontal line

• A vertical line

Answer explanation

A line with a negative slope decreases as it moves from left to right. Therefore, the correct description is 'A line slanting downwards from left to right', indicating a negative slope.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

CCSS.8.F.B.5

A line with a 0 slope is:

• Vertical

• Horizontal

• Diagonal

• Curved

Answer explanation

A line with a 0 slope is horizontal because it runs parallel to the x-axis, indicating that there is no vertical change as you move along the line. Therefore, the correct answer is 'Horizontal'.

Which of the following lines has an undefined slope?

• A horizontal line

• A vertical line

• A diagonal line

• A curved line

Answer explanation

A vertical line has an undefined slope because it does not run horizontally; instead, it goes straight up and down, resulting in a division by zero when calculating slope (change in y over change in x).

In point-slope form, the equation of a line with slope m that passes through the point (x_1, y_1) is y - y_1 = m(x - x_1). Match the description of each line with the correct equation.

• y + 3 = 4(x + 2)

• slope = 4, passes through point (2, -3)

• y - 3 = 4(x - 2)

• slope = 4, passes through point (-2, 3)

• y + 3 = 4(x - 2)

• slope = 4, passes through point (-2, -3)

• y - 3 = 4(x + 2)

• slope = 4, passes through point (2, 3)

Rewrite the equation (y - 4) = 3(x + 2) in slope intercept form.

• y = 3x + 10

• y = 3x - 10

• y = -3x + 10

• y = -3x - 10

Answer explanation

To rewrite (y - 4) = 3(x + 2) in slope-intercept form, distribute: y - 4 = 3x + 6. Then, add 4 to both sides: y = 3x + 10. Thus, the correct answer is y = 3x + 10.

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Rewrite the equation (y - 4) = 3(x + 2) in Standard Form.

• 3x - y = -10

• 3x + y = 10

• 3x - y = 10

• 3x + y = -10

Answer explanation

To rewrite (y - 4) = 3(x + 2) in standard form, first distribute: y - 4 = 3x + 6. Then, rearrange to get 3x - y = -10, which matches the correct choice: 3x - y = -10.

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Rewrite (y - 3) = 4(x - 6) in slope intercept form.

• y = 4x - 21

• y = 4x + 21

• y = -4x + 21

• y = 4x - 9

Answer explanation

To rewrite (y - 3) = 4(x - 6) in slope-intercept form, first distribute: y - 3 = 4x - 24. Then, add 3 to both sides: y = 4x - 21. Thus, the correct answer is y = 4x - 21.

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Rewrite (y - 3) = 4(x - 6) in standard form.

• 4x - y = 21

• 4x + y = 21

• 4x - y = -21

• 4x + y = -21

Answer explanation

To rewrite (y - 3) = 4(x - 6), first distribute: y - 3 = 4x - 24. Then, add 3 to both sides: y = 4x - 21. Rearranging gives 4x - y = 21, which is in standard form. Thus, the correct answer is 4x - y = 21.