Section 2.3 - Quick Graphs of Linear Equations ALGEBRA TWO Section 2.3 - Quick Graphs of Linear Equations

LEARNING GOALS Goal One - Use the slope-intercept form of a linear equation to graph linear equations. Goal Two - Use the standard form of a linear equation to graph linear equations.

VOCABULARY If the graph of an equation intersects the y-axis at the point (0, b), then the number b is the y-intercept. The slope-intercept form of a linear equation is y = mx + b. 1

Graphing Equations in Slope-Intercept Form The slope-intercept form of an equation gives you a quick way to graph the equation. STEP 1: Write the equation in slope-intercept form by solving for y. STEP 2: Find the y-intercept and use it to plot the point where the line crosses the y-axis. STEP 3: Find the slope and use it to plot a second point on the line. STEP 4: Draw a line through the two points. 1

Graphing Equations in Slope-Intercept Form PROBLEM: Graph 2x + y = 3 SOLUTION STEP 1: Write equation in slope-intercept form. 2x + y = 3 Write original equation y = -2x + 3 Subtract 2x from each side STEP 2: The y-intercept is 3, so plot the point (0, 3).

Graphing Equations in Slope-Intercept Form PROBLEM: Graph 2x + y = 3 SOLUTION STEP 3: The slope is -2/1, so plot a second point by moving 1 unit to the left and 2 units up. This point is (-1, 5).

Graphing Equations in Slope-Intercept Form PROBLEM: Graph 2x + y = 3 SOLUTION STEP 4: Draw a line through the two points.

VOCABULARY The standard-form of a linear equation is Ax + By = C, where A and B are not both zero. The y-intercept is the y-coordinate of the point where the graph crosses the y-axis and is found by letting x = 0 and solving for y. The x-intercept is the x-coordinate of the point where the graph crosses the x-axis and is found by letting y = 0 and solving for x. 1

Graphing Equations in Standard Form The standard form of an equation gives you a quick way to graph the equation. STEP 1: Write the equation in standard form. STEP 2: Find the x-intercept by letting y = 0 and solving for x. Use the x-intercept to plot the point where the line crosses the x-axis. STEP 3: Find the y-intercept by letting x = 0 and solving for y. Use the y-intercept to plot the point where the line crosses the y-axis. STEP 4: Draw a line through the two points. 1

PROBLEM: Graph -2x +3y = -6 Graphing with the Standard Form SOLUTION STEP 1: The equation is in standard form. -2x + 3y = -6 STEP 2: Find the x-intercept. -2x + 3(0) = -6 Substitute 0 for y. -2x/-2 = -6/-2 Divide each side by -2 x = 3 Simplify The x-intercept is (3, 0) 1

Graphing with the Standard Form STEP 3: Find the y-intercept. PROBLEM: Graph -2x +3y = -6 SOLUTION STEP 3: Find the y-intercept. -2(0) + 3y = -6 Substitute 0 for x. 3y/3 = -6/3 Divide each side by 3 y = -2 Simplify The y-intercept is (0, -2) 1

PROBLEM: Graph -2x +3y = -6 Graphing with the Standard Form SOLUTION STEP 4: Draw a line through the two points (3, 0) and (0, -2). 1

Using the Standard Form PROBLEM: Sales for the firefighters benefit dinner were $1980. The cost for a child’s dinner was $4.50 and an adult’s dinner was $6.00. Describe the number of children and adults who attended to reach this amount. SOLUTION WRITE A VERBAL MODEL. TIMES Cost per child Number of children PLUS Cost per adult TIMES Number of adults EQUALS Total Revenue

Using the Standard Form WRITE AN ALGEBRAIC MODEL. PROBLEM: Sales for the firefighters benefit dinner were $1980. The cost for a child’s dinner was $4.50 and an adult’s dinner was $6.00. Describe the number of children and adults who attended to reach this amount. SOLUTION WRITE AN ALGEBRAIC MODEL. 4.50c + 6.00a = 1980 The graph of this equation is a line that intersects the c-axis at (440, 0) and the a-axis at (0, 330). Points along this line represent the number of combinations of people that could have attended.

Review slope-intercept form of a linear equation is y = mx + b. STEP 1: Write the equation in slope-intercept form by solving for y. STEP 2: Find the y-intercept and use it to plot the point where the line crosses the y-axis. STEP 3: Find the slope and use it to plot a second point on the line. STEP 4: Draw a line through the two points. standard-form of a linear equation is Ax + By = C, where A and B are not both zero. STEP 1: Write the equation in standard form. STEP 2: Find the x-intercept by letting y = 0 and solving for x. Use the x-intercept to plot the point where the line crosses the x-axis. STEP 3: Find the y-intercept by letting x = 0 and solving for y. Use the y-intercept to plot the point where the line crosses the y-axis. STEP 4: Draw a line through the two points.

Homework pg. 86-88. # 21, 23, 25, 29, 31, 35, 41, 45, 49, 57