Quick Graphing Using Slope-Intercept Form

43210 In addition to level 3.0 and above 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 understand that linear relationships can be described using multiple representations. - Represent and solve equations and inequalities graphically. - Write equations in slope-intercept form, point-slope form, and standard form. - Graph linear equations and inequalities in two variables. - Find x- and y- intercepts. The student will be able to: - Calculate slope. - Determine if a point is a solution to an equation. - Graph an equation using a table and slope- intercept form. With help from the teacher, the student has partial success with calculating slope, writing an equation in slope- intercept form, and graphing an equation. Even with help, the student has no success understanding the concept of a linear relationships. Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.F- IF.C.7, HS.F-LE.A.2): The student will understand that linear relationships can be described using multiple representations.

What are the different methods we have used to graph a line? Plot points Make a table Find the x and y- intercepts Plot a point then graph the slope.

Slope-intercept form: linear equation y = mx+b m represents the slope of the line b represents the y-intercept *where the line crosses the y-axis

You can tell by looking at the equation not only where the line crosses y, but whether it has a positive or negative slope. If m is positive the slope is positive, and your line will go up from left to right. If m is negative, the slope is negative and your line will go down from left to right. y = mx + b

Determine what is the slope, y-intercept, and direction of each equation. 1.y = 3x y = ½ x – 9 3.y = - 4 / 5 x y = -2x Slope = 3 y-intercept = (0, 4) goes up left to right 2.Slope = ½ y-intercept = (0, -9) goes up left to right 3.Slope = - 4 / 5 y-intercept = (0, 7) goes down left to right 4.Slope = -2 y-intercept = (0, -4) goes down left to right

When your equation is not in slope intercept form, rewrite it into slope-intercept form (y=mx+b). 2x = 5y x = 5y-10 -5y -5y 2x – 5y = x -2x -5y = -2x – y = 2 / 5 x + 2 What is the y- intercept? (0,2) What is the slope? 2/52/5 What direction will the line go? Up, from left to right.

Graph the line y = 2 / 5 x + 2 The slope is 2 / 5 & the y-intercept is Steps to graphing a line in slope intercept form: 1.Plot the y- intercept. (0,2) 2.Count up 2 right 5 and plot next point. 3.Connect the dots.

Graph the line 2y = -2x Change to slope intercept form. 2.y = -x y-intercept (0,3) 4.Slope -1 5.Line will go down from left to right

Special line: Parallel Lines: lines have the same slope, but different y- intercept (b value) y = 2x + 4 and y = 2x – 3 are parallel lines.

Graph y = -x+6 and y = -x+2 on the same graph. Notice that they each have the same slope of -1, but they cross y at different spots.

y = -x + 6 y = -x + 2