4.3 Graphing Linear Nonproportional Relationships Using Slope and y-intercept How can you graph a line using the slope and y-intercept?

Texas Essential Knowledge and Skills The student is expected to: Proportionality—8.5.B Represent linear nonproportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0. Mathematical Processes 8.1.E Create and use representations to organize, record, and communicate mathematical ideas.

ADDITIONAL EXAMPLE 1 Graph each equation. A y = 3x + 2 B y = x – 2

ADDITIONAL EXAMPLE 2 A shipping company charges a fixed amount plus a certain amount per pound to ship a package. The total cost y, in dollars, to ship a package is given by the equation y = 3x + 5, where x is the weight of the package in pounds. A Graph the equation.

ADDITIONAL EXAMPLE 2 A shipping company charges a fixed amount plus a certain amount per pound to ship a package. The total cost y, in dollars, to ship a package is given by the equation y = 3x + 5, where x is the weight of the package in pounds. B What is the weight of a package that can be shipped for $17? 4 lb

4.3 LESSON QUIZ 8.5.B 1. Graph the equation y = x – 2.

2. Maria is ordering comic books online. The equation y = 8x + 4 represents the total cost in dollars, y, including shipping, for ordering x number of comic books. a. Graph the equation. b. If the total cost including shipping is $60, how many comic books is Maria ordering? 7 comic books

3. Mr. Goldstein is driving to Houston. The equation y = –45x + 270 represents the numbers of miles that he still has to travel after driving for x hours. Find and interpret the slope and y-intercept of the line that represents this situation. Slope = –45; y-intercept = 270; he is driving 45 miles per hour and at the beginning, had 270 miles to drive.

Have students use graphing calculators to graph on the same set of axes three linear equations whose graphs have the same slope. For example, have them graph y = 2x, y = 2x + 3, and y = 2x – 4. Then have them graph, on a new pair of axes, another set of linear equations whose graphs have the same slope, but different from the slope of the first set of lines. For example, have them graph y = –3x, y = –3x + 2, and y = –3x – 1. Ask students to make a conjecture about lines with the same slopes (they are parallel). Have them try out other sets of linear equations to test their conjectures.

How can you graph a line using the slope and y-intercept? Sample answer: First, plot the point that contains the y-intercept. Then use the slope to find another point on the line and draw a line through the points.