Graph with Slopes & y-Intercepts

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Presentation transcript:

Graph with Slopes & y-Intercepts Learn to use slopes and y-intercepts to graph linear equations.

Focus 7 - Learning Goal #1: The student will understand the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities. 4 3 2 1 In addition to level 3.0 and beyond what was taught in class, the student may: Make connection with other concepts in math. Make connection with other content areas. The student will demonstrate and explain the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities. The student will demonstrate and identify proportional relationships, lines, and linear equations and use functions to model quantities. With help from the teacher, the student has partial success with level 2 and 3 elements. Even with help, students have no success with level 2 and 3 content.

In an equation written in slope-intercept form, y = mx + b, m is the slope and b is the y-intercept.

y = mx + b The y-intercept is where the line crosses the y-axis. This is the vertical axis. The y-intercept is written as an ordered pair (0, y). The y-intercept of y = 2x + 1 is (0, 1) The y-intercept of y = 2x – 3 is (0, -3)

y = mx + b The slope tells us how steep the line is. If m is positive, the line will go up from left to right. If m is negative, the line will go down from left to right. The slope of y = 2x + 1 is 2 (Do NOT write the x after the 2.) The slope of y = -1/2x – 3 is - ½

y = 3x + 4 y = ½ x – 9 y = -4/5 x + 7 y = -2x - 4 Determine what is the slope, y-intercept, and direction of each equation. Slope = 3 y-intercept = (0, 4) goes up left to right Slope = ½ y-intercept = (0,-9) goes up left to right Slope = -4/5 y-intercept = (0,7) goes down left to right Slope = -2 y-intercept = (0,-4) goes down left to right y = 3x + 4 y = ½ x – 9 y = -4/5 x + 7 y = -2x - 4

Graph the line y = 2/5x + 2 The slope is 2/5 & the y-intercept is (0, 2). Steps to graphing a line in slope intercept form: Plot the y-intercept. (0,2) Count up 2, right 5 and plot next point. Connect the dots.

Graph the line y = -x + 3 Plot the y-intercept (0, 3) Slope -1 Count down 1, right 1. Line will go down from left to right.

Graph the line y = 2/3x + 4 Plot the y-intercept (0, 4) Slope 2/3 Count up 2, right 3. Line will go up from left to right.

“y = mx + b” video