Standard Form Examples 3x + y = 5 -2x + y = 10 x – y = 6

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Presentation transcript:

Standard Form Examples 3x + y = 5 -2x + y = 10 x – y = 6 ALGEBRA 1 LESSON 6-3 ) Examples 3x + y = 5 -2x + y = 10 x – y = 6 20x + 4y = 8 9x - 3y = 1 2x + 5y = 4 8-5

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 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. 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 8-5

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. 8-5

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. 8-5

Standard Form Write y = x + 6 in standard form using integers. 2 ALGEBRA 1 LESSON 6-3 Write y = x + 6 in standard form using integers. 2 3 y = x + 6 2 3 3y = 3( x + 6 ) Multiply each side by 3. 3y = 2x + 18 Use the Distributive Property. –2x + 3y = 18 Subtract 2x from each side. The equation in standard form is –2x + 3y = 18. 8-5

Standard Form ALGEBRA 1 LESSON 6-3 Write an equation in standard form to find the number of hours you would need to work at each job to make a total of $130. Define: Let = the hours mowing lawns. Let = the hours delivering newspapers. x y Amount Paid per hour Job Mowing lawns $12 Delivering newspapers Relate: $12 per h plus $5 per h equals $130 mowing delivering $5 Write: 12 + 5 = 130 x y The equation standard form is 12x + 5y = 130. 8-5

Standard Form Find each x- and y-intercepts of each equation. ALGEBRA 1 LESSON 6-3 Find each x- and y-intercepts of each equation. 1. 3x + y = 12 2. –4x – 3y = 9 3. Graph 2x – y = 6 using x- and y-intercepts. For each equation, tell whether its graph is horizontal or vertical. 4. y = 3 5. x = –8 6. Write y = x – 3 in standard form using integers. x = – , y = –3 9 4 x = 4, y = 12 horizontal vertical 5 2 –5x + 2y = –6 or 5x – 2y = 6 8-5