Meaning of Slope for Equations, Graphs, and Tables Section 1.4 Meaning of Slope for Equations, Graphs, and Tables

Find the slope of the line Finding Slope from a Linear Equation Finding Slope from a Linear Equation Example Find the slope of the line Solution x y 0 1 3 5 3 7 Create a table using x = 1, 2, 3. Then sketch the graph. Section 1.4 Slide 2

Note the following three observations about the slope of the line Finding Slope from a Linear Equation Finding Slope from a Linear Equation Observations Note the following three observations about the slope of the line The coefficient of x is 2, which is the slope. If the run is 1, then the rise is 2. As the value of x increases by 1, the value of y increases by 2. Section 1.4 Slide 3

Find the slope of the line Finding Slope from a Linear Equation Finding Slope from a Linear Equation Example Find the slope of the line Solution x y 0 8 5 2 3 –1 Create a table using x = 1, 2, 3. Then sketch the graph. Section 1.4 Slide 4

For the line , if the run is 1, then the rise is m. Vertical Change Property Vertical Change Property Property For the line , if the run is 1, then the rise is m. Vertical Change property for a positive slope. Vertical Change property for a negative slope. Section 1.4 Slide 5

Finding the y-intercept of a Linear Line Finding the y-Intercept of linear Equation Sketching Equations: It’s helpful to know the y-intercept. y-intercept has a x-value of 0. Substitute x = 0 gives Property For a linear equation of the form , the y- intercept is (0, b). Section 1.4 Slide 6

What is the y-intercept of Finding the y-intercept of a Linear Line Finding the y-Intercept of linear Equation Example What is the y-intercept of Solution b is equal to 3, so the y-intercept is (0, 3) Definition If an equation of the form , we say that it is in slope-intercept form. Section 1.4 Slide 7

Graphing Linear Equations Example Sketch the graph of y = 3x – 1. Solution The y-intercept is (0, –1) and the slope is To graph: Plot the y-intercept, (0, 1). (continued) Section 1.4 Slide 8

Graphing Linear Equations Solution Continued From (0, –1), look 1 unit to the right and 3 units up to plot a second point, which we see by inspection is (1, 2). Sketch the line that contains these two points. Section 1.4 Slide 9

Graphing Linear Equations Guidelines To sketch the graph of a linear equation of the form Plot the y-intercept (0, b). Use m = to plot a second point. Sketch the line that passes through the two plotted points. Section 1.4 Slide 10

Graphing Linear Equations Example Sketch the graph of 2x + 3y = 6. Solution First we rewrite into slope-intercept form: Original Equation Subtract 2x from both sides. Combine & rearrange terms Divide both sides by 3. Section 1.4 Slide 11

Graphing Linear Equations Solution Continued y-intercept: (0, 2) Slope: Plot the y-intercept, (0, 2). 2. From the point (0, 2), look 3 units to the right and 2 units down to plot a second point, which we see by inspection is (3, 0). Section 1.4 Slide 12

Graphing Linear Equations Solution Continued 3. Then sketch the line that contains these two points. We can verify our result by checking that both (0, 2) and (3, 0) are solutions. Section 1.4 Slide 13

Slope Addition Property Example For the following sets, is there a line that passes through them? If so, find the slope of that line. Solution Value of x increases by 1. Value of y changes by –3. The slope is –3. Section 1.4 Slide 14

Slope Addition Property Solution Continued Set 2 Value of x increases by 1. Value of y changes by 5. So, the slope is 5. Set 3 Value of y does not change by the same value. Hence, not a line. Section 1.4 Slide 15