Lesson 6-3 (Part 1) Standard Form page 298 Objective: To graph equations using intercepts.

Real-World Connection We can use an equation to model a situation that involves exercise, as in example 5.

where A, B, and C are real numbers and DEFINITION Standard form of a linear equation: Ax + By = C where A, B, and C are real numbers and A and B are not zero. x-intercept—the x-coordinate of the point where a line crosses the x-axis y-intercept– the y-coordinate of the point where a line crosses the y-axis

Standard Form Find the x- and y-intercepts of 2x + 5y = 6. ALGEBRA 1 LESSON 6-3 Find the x- and y-intercepts of 2x + 5y = 6. Step 2  To find the y-intercept, substitute 0 for x and solve for y. 2x + 5y = 6 2(0) + 5y = 6 5y = 6 y = The y-intercept is . 6 5 Step 1  To find the x-intercept, substitute 0 for y and solve for x. 2x + 5y = 6 2x + 5(0) = 6 2x = 6 x = 3 The x-intercept is 3. 6-3

Example 1, page 299 Find the x and y intercept of 3x + 4y = 8.

Example 1, page 299 Find the x-and y-intercepts of 4x – 9y = -12.

Graphing Using Intercepts Find the x-intercept by substituting zeros for y. Find the y-intercept by substituting zeros for x. Plot the intercepts. Draw the line.

Standard Form Graph 3x + 5y = 15 using intercepts. ALGEBRA 1 LESSON 6-3 Graph 3x + 5y = 15 using intercepts. Step 1  Find the intercepts. 3x + 5y = 15 3x + 5(0) = 15 Substitute 0 for y. 3x = 15 Solve for x. x = 5 3(0) + 5y = 15 Substitute 0 for x. 5y = 15 Solve for y. y = 3 Step 2  Plot (5, 0) and (0, 3). Draw a line through the points. 6-3

Example 2, page 299 Graph 2x + 3y = 12 using the x- and y-intercepts. 5 -5

Example 2, page 299 Graph 5x + 2y = -10 using the x- and y-intercepts. -5

either A or B = 0, but not both. Special Lines In standard form Ax + By = C either A or B = 0, but not both. If A = 0, the line is horizontal and the equation looks like: y = #. If B = 0, the line is vertical and the equation looks like: x = #.

Standard Form a. Graph y = 4 b. Graph x = –3. ALGEBRA 1 LESSON 6-3 a. Graph y = 4 b. Graph x = –3. 0 • x + 1 • y = 4 Write in standard form. For all values of x, y = 4. 1 • x + 0 • y = –3 Write in standard form. For all values of y, x = –3. 6-3

Example 3, page 299 Graph each equation. a) y = -3 b) x = 2 y x 5 -5 y x 5 -5

Example 3, page 299 Graph each equation. a) y = 5 b) y = 0 y x 5 -5 y x 5 -5

Example 3, page 299 Graph each equation. c) x = -4 d) x = 0 y x 5 -5 y x 5 -5

Summary What did you learn today?

SUMMARY Standard form of an equation is Ax + By = C A horizontal line has equation y = #. A vertical line has equation x = #.

ASSIGNMENT Lesson 6-3 page 301 #1-26 all, 70-78 all