Do Now 11/28/11 In your notebook, explain if the equations below are the same line. y – 5 = 3(x + 2) y – 2 = 3(x + 5) y = 3x + 11 y = 3x + 17 No No y –

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Do Now 11/28/11 In your notebook, explain if the equations below are the same line. y – 5 = 3(x + 2) y – 2 = 3(x + 5) y = 3x + 11 y = 3x + 17 No No y – 3 = 2(x – 1) y + 3 = 2(x + 2) y = 2x + 1 Yes Yes

Objective 5.4 write linear equations in standard form.

Section 5.4 “Write Linear Equations in Standard Form” The STANDARD FORM of a linear equation is represented as Ax + By = C where A, B, and C are real numbers

To write another equivalent equation, multiply each side by x – 12y = 8 To write one equivalent equation, multiply each side by 2. SOLUTION Write two equations in standard form that are equivalent to 2x – 6y = 4. x – 3y = 2

y – y 1 = m(x – x 1 ) Calculate the slope. STEP 1 – 3– 3– 3– 3 m =m =m =m = 1 – (–2) 1 –2 1 –2 = 3 –1 = Write an equation in point-slope form. Use (1, 1). Write point-slope form. y – 1 = – 3(x – 1) Substitute 1 for y 1, - 3 for m and 1 for x 1. Write an equation in standard form of the line shown. STEP 2 Rewrite the equation in standard form. 3x + y = 4 Simplify. Collect variable terms on one side, constants on the other. STEP 3

y – y 1 = m(x – x 1 ) Calculate the slope. STEP 1 2 m =m =m =m = -3 – (–1) 2 –3 2 –3 = = Write an equation in point-slope form. Use (3, -1). Write point-slope form. STEP 2 Rewrite the equation in standard form. -2x + y = -7 Simplify. Collect variable terms on one side, constants on the other. STEP 3 Write an equation in standard form of the line that passes through the points (3, -1) and (2, -3). y + 1 = 2(x – 3) Substitute 3 for x 1, –1 for y 1 and 2 for m.

SOLUTION Write an equation of the specified line. The y- coordinate of the given point on the blue line is –4. This means that all points on the line have a y- coordinate of –4. An equation of the line is y = –4. a.a.a.a. The x- coordinate of the given point on the red line is 4. This means that all points on the line have an x- coordinate of 4. An equation of the line is x = 4. b.b.b.b. Blue line a.a.a.a. Red line b.b.b.b.

SOLUTION The y- coordinate of the given point is –5. This means that all points on the line have a y- coordinate of –5. An equation of the line is y = –5. The x- coordinate of the given point is 13. This means that all points on the line have an x -coordinate of 13. An equation of the line is x = 13. Write an equation of the horizontal and vertical lines that pass through the given point. (13, –5) STEP 1 STEP 2

Simplify. Find the value of A. Substitute the coordinates of the given point for x and y in the equation. Solve for A. STEP 1 SOLUTION Find the missing coefficient in the equation of the line shown. Write the completed equation. Ax + 3y = 2 A(–1) + 3(0) = 2 –A = 2 A = – 2 Write equation. Substitute – 1 for x and 0 for y. Divide by – 1. Complete an equation in standard form Complete the equation. – 2x + 3y = 2 Substitute – 2 for A. STEP 2

Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation. Ax + y = –3, (2, 11) Simplify. Find the value of A. Substitute the coordinates of the given point for x and y in the equation. Solve for A. STEP 1 Ax + y = -3 A(2) + (11) = -3 2A = -14 A = –7 Write equation. Substitute 2 for x and 11 for y. Divide by 2. Complete the equation. STEP 2 – 7x +y = –3 Substitute –7 for A.