Objective: To graph lines given their equations.

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Objective - To graph linear equations using the slope and y-intercept.

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Presentation transcript:

Objective: To graph lines given their equations. Chapter 3 Lesson 5 Objective: To graph lines given their equations.

y = mx + b y-intercept slope Slope-Intercept Form: a linear equation y=mx+b, where m is the slope of the line and b is the y-intercept. y = mx + b y-intercept slope **Remember: Postulate 1-1 states that two points determine a line.**

Example 1: Graphing Lines in Slope-Intercept Form 2 4 6 8 -2 -4 -6 Move right 4 units Graph the line Move up 3 units Start at (0,2) Slope y-intercept

Example 2: Graphing Lines in Slope-Intercept Form 4 6 8 -2 -4 -6 Graph the line Start at (0,-2) Slope y-intercept Move right 2 units Move down 1 unit

Example 3: Graphing Lines in Slope-Intercept Form 2 4 6 8 -2 -4 -6 Start at (0,9) Move down 2 units Use the slope and y-intercept to graph the line y=-2x+9 or Move right 1 unit Slope y-intercept

Example 4: Graphing Lines Using Intercepts standard form of a linear equation: Ax+By=C, where A,B, and C are real numbers and A and B are not both zero. Example 4: Graphing Lines Using Intercepts Graph 6x + 3y = 12 Step 2: To find the x-intercept substitute 0 for y; solve for x. Step 1: To find the y-intercept substitute 0 for x; solve for y. 6x + 3y = 12 6(0) + 3y = 12 3y = 12 y = 4 (0,4) 6x + 3y = 12 6x + 3(0) = 12 6x = 12 x = 2 (2,0)

Example 4 (cont.): Graphing Lines Using Intercepts 2 4 6 8 -2 -4 -6

Example 5: Graphing Lines Using Intercepts Graph -2x + 4y = -8 Step 2: To find the x-intercept substitute 0 for y; solve for x. Step 1: To find the y-intercept substitute 0 for x; solve for y. -2x + 4y = -8 -2(0) + 4y = -8 4y = -8 y = -2 (0,-2) -2x + 4y = -8 -2x + 4(0) = -8 -2x = -8 x = 4 (4,0)

Example 5 (cont.) : Graphing Lines Using Intercepts 2 4 6 8 -2 -4 -6

Example 6: Transforming to Slope-Intercept Form Graph 4x - 2y = 9 Step 1: Transform the equation to slope-intercept form. y=mx+b Slope y-intercept

Example 6 (cont.) : Transforming to Slope-Intercept Form 2 4 6 -2 -4 -6 Step 2: Use the y-intercept and the slope to plot two points and draw the line containing them. Slope y-intercept

Example 7: Transforming to Slope-Intercept Form Transform the equation -6x + 3y = 12 to slope-intercept form, and then graph the resulting equation. Step 1: Transform the equation to slope-intercept form. y=mx+b Slope y-intercept

Example 7 (cont.) : Transforming to Slope-Intercept Form 2 4 6 8 -2 -4 Step 2: Use the y-intercept and the slope to plot two points and draw the line containing them. Slope y-intercept

Homework Page 155 – 156 #1-16; 33 -38; 45-46; 48-51