Day 8

Student Packet

Summer 2013

Determining Slope and Intercepts

Intensive Math-Algebra I Mini-Lesson MA.912.A.3.9

Summer 2013 Intensive Mathematics – Algebra 1 Day 8

Name: _____________________________________________________ Date: __________________

Benchmark MA.912.A.3.9

Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the

line.

This benchmark will be assessed using MC and FR items.

Students will: • Determine the slope, x-intercept, and/or y-intercept of a line given its graph, its equation, or two

points on the line. Content Limits

• Items may include lines that have zero slope or undefined slope.

Stimulus Attributes: • Items may include linear equations in various forms, including standard, slope-intercept, and point-

slope forms. • Graphics should be used in most of these items, as appropriate. • Fill-in response items may require that students provide a slope, the x-coordinate of the x-intercept,

the y-coordinate of the y-intercept, or the x-coordinate or y-coordinate of a point of interest. Lesson MA.912.A.3.9 Textbook: Prentice Hall Algebra 1 I can …

• Determine the slope of a line given its graph, equation, or 2 points on the line. • Determine the intercepts of a line given its graph, equation, or 2 points on the line.

Vocabulary

• Slope • Intercepts • Axis • Standard Form • Slope-Intercept Form • Point-Slope Form • Coordinate

Essential Understanding

• You can use any two points on a line to find its slope.

• Graphs of linear functions may cross the y-axis and/or the x-axis at any point.

• A y-intercept of a graph is the y-coordinate of a point where the graph crosses the y-axis.

• The x-intercept is the x-coordinate of a point where the graph crosses the x-axis.

• Any point on the y-axis has a x-coordinate of 0, (0,y).

• Any point on the x-axis has a y-coordinate of 0, (x, 0).

Summer 2013 Intensive Mathematics – Algebra 1 Day 8

Example # 1: Textbook page 293

Guided Practice: Textbook page 296: 14 - 16

Example # 2: Textbook page 294

Example # 3: Textbook page 294

Guided Practice: Textbook page 296: 20 - 25

Example # 4: Textbook page 307

Example # 3: Textbook page 320

Guided Practice: Textbook page 310: 11 – 14, and page 324: 11 – 13

Small Group Practice: Focus MA912A39

Mini-Assessment MA912A39 Score: ____________

Home Learning: HL MA912A39

Summer 2013 Intensive Mathematics – Algebra 1 Day 8

Focus Practice MA.912.A.3.9

1. Carla is one year older than James. The relationship between their ages can be represented by the equation

C = J + 1 If Carla's age is graphed as a function of James's age, what will be the coordinates of the x- and y-intercepts for the graph of this function?

2. On a coordinate graph, Celeste places a red marble at the point (2, 2) and a green marble at the point (4, 1). If she draws a line that passes through both of these points, which set of coordinates represents the x- and y-intercepts of the line?

3. The graph below shows the rate at which a cross-country runner burns calories. What is the slope of the line?

4. The diagram below shows the dimensions of Lopez family's house. What is the slope of the portion of the roof that is represented by the solid black line?

Summer 2013 Intensive Mathematics – Algebra 1 Day 8

5. The equation 3x − 2y = −16 can be used to determine the size of a recommended refrigerator, where y

represents the volume of the refrigerator in cubic feet, and x represents the number of people (greater

than 2) living in the residence. When this equation is graphed on a coordinate plane, where does the

line intercept the y-axis?

6. Armando is two years younger than Rosa. The relationship between their ages can be represented by

the equation

A = R − 2

If Armando's age is graphed as a function of Rosa's age, what will be the coordinates of the x- and y-

intercepts for the graph of this function?

7. On a coordinate graph, Andrew places a paperclip at the point (2, 4) and a thumbtack at the point (3,

2). If he draws a line that passes through both of these points, which set of coordinates represents the

x- and y-intercepts of the line?

8. The graph below shows how the US Census Bureau expects the population of the United States of

America to grow over the next few decades. What is the slope of the line?

Summer 2013 Intensive Mathematics – Algebra 1 Day 8

9. The diagram below shows the dimensions of a company's warehouse. What is the slope of the ramp,

represented by the solid black line?

10. The equation 4y + 2x = 660 can be used to determine the target heart rate of a person, where x

represents the target heart rate and y represents the person's age. When this equation is graphed on a

coordinate plane, where does the line intercept the y-axis?

Summer 2013 Intensive Mathematics – Algebra 1 Day 8

Home Learning

MA.912.A.3.9: Determine slope, x-intercept, and y-intercept.

1. What is the x-intercept of the equation ?

A.

B.

C.

D.

2. A line contains points (4, 7) and (-3, 2). What is the slope of the line?

A.

B.

C.

D.

3. The graph of a line contains the points and

Which of the following must be true about the graph of this line?

A. The line has no slope.

B. The slope of the line is negative.

C. The slope of the line is positive.

D. The line does NOT intersect the x-axis.

4. Find the x- and y-intercept of the line:

A. x-intercept is -8; y-intercept is 40

B. x-intercept is 1; y-intercept is -5

C. x-intercept is -5; y-intercept is 1

D. x-intercept is 40; y-intercept is -8

Summer 2013 Intensive Mathematics – Algebra 1 Day 8

5. Find the slope of the line described by – – .

A.

B.

C.

D.

6. Find the x- and y-intercepts of

A. x-intercept: -11, y-intercept: 4

B. x-intercept: –8, y-intercept: 3

C. x-intercept: -11, y-intercept: 3

D. x-intercept: –8, y-intercept: 4

7. The graph of line is shown below.

What is the slope of line in its simplest fractional form?

A.

B.

C.

D.