# Using Slopes and Intercepts

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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)

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.

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.

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.