Using Slopes and Intercepts Course 3 12-3 Using Slopes and Intercepts Warm Up Find the slope of the line that passes through each pair of points (3, 6) and (–1, 4) 2. (1, 2) and (6, 1) 4-6 -2 1 -1-3 -4 2 – 1-2 -1 6-1 5

Using Slopes and Intercepts Course 3 12-3 Using Slopes and Intercepts Learn to use slopes and intercepts to graph linear equations.

Insert Lesson Title Here Course 3 12-3 Using Slopes and Intercepts Insert Lesson Title Here Vocabulary x-intercept y-intercept slope-intercept form

Using Slopes and Intercepts Course 3 12-3 Using Slopes and Intercepts You can graph a linear equation easily by finding the x-intercept and the y-intercept. The x-intercept of a line is the value of x where the line crosses the x-axis (where y = 0). The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0).

Using Slopes and Intercepts Course 3 12-3 Using Slopes and Intercepts Additional Example 1: Finding x-intercepts and y-intercepts to Graph Linear Equations Find the x-intercept and y-intercept of the line 4x – 3y = 12. Use the intercepts to graph the equation. Find the x-intercept (y = 0). 4x – 3y = 12 4x – 3(0) = 12 4x = 12 4x 4 12 = x = 3 The x-intercept is 3.

Additional Example 1 Continued Course 3 12-3 Using Slopes and Intercepts Additional Example 1 Continued Find the y-intercept (x = 0). 4x – 3y = 12 4(0) – 3y = 12 –3y = 12 –3y –3 12 = y = –4 The y-intercept is –4.

Additional Example 1 Continued Course 3 12-3 Using Slopes and Intercepts Additional Example 1 Continued The graph of 4x – 3y = 12 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, –4).

Using Slopes and Intercepts Course 3 12-3 Using Slopes and Intercepts The form Ax + By = C, where A, B, C are real numbers, is called the Standard Form of a Linear Equation. Helpful Hint

y = mx + b Using Slopes and Intercepts 12-3 Course 3 12-3 Using Slopes and Intercepts In an equation written in slope-intercept form, y = mx + b, m is the slope and b is the y-intercept. y = mx + b Slope y-intercept

Using Slopes and Intercepts Course 3 12-3 Using Slopes and Intercepts Additional Example 2A: Using Slope-Intercept Form to Find Slopes and y-intercepts Write each equation in slope-intercept form, and then find the slope and y-intercept. 2x + y = 3 2x + y = 3 –2x –2x Subtract 2x from both sides. y = 3 – 2x Rewrite to match slope-intercept form. y = –2x + 3 The equation is in slope-intercept form. m = –2 b = 3 The slope of the line 2x + y = 3 is –2, and the y-intercept is 3.

Additional Example 4: Writing Slope-Intercept Form Course 3 12-3 Using Slopes and Intercepts Additional Example 4: Writing Slope-Intercept Form Write the equation of the line that passes through (3, –4) and (–1, 4) in slope-intercept form. Find the slope. = y2 – y1 x2 – x1 4 – (–4) –1 – 3 8 –4 = = –2 The slope is –2. Substitute either point and the slope into the slope-intercept form. y = mx + b Substitute –1 for x, 4 for y, and –2 for m. 4 = –2(–1) + b 4 = 2 + b Simplify.

Additional Example 4 Continued Course 3 12-3 Using Slopes and Intercepts Additional Example 4 Continued Solve for b. 4 = 2 + b –2 –2 Subtract 2 from both sides. 2 = b Write the equation of the line, using –2 for m and 2 for b. y = –2x + 2

Using Slopes and Intercepts Insert Lesson Title Here Course 3 12-3 Using Slopes and Intercepts Insert Lesson Title Here Lesson Quiz Write each equation in slope-intercept form, and then find the slope and y-intercept. 1. 2y – 6x = –10 Write the equation of the line that passes through each pair of points in slope-intercept form. 3. (0, 2) and (4, –1) y = 3x – 5; m = 3; b = –5 y = – x + 2 3 4