Daily Homework Quiz 1 Review 5 3 Write

Daily Homework Quiz 1. Review 5. 3 Write an equation in point-slope form of the line that passes through (6, – 4) and has slope 2. y – y 1 = m(x – x 1) ANSWER 2. y + 4 = 2(x – 6) Write an equation in point-slope form of the line that passes through (– 1, – 6) and (3, 10). ANSWER y + 6 = 4(x + 1) or y – 10 = 4(x– 3)

Review 5. 3 Write an equation in point-slope form of the line that passes through the given points. 1. (1, 4), (6, – 1) ANSWER NOW PUT EACH ANSWER IN SLOPE-INTERCEPT FORM!! or y – 4 = – 1(x – 1) or y– 4= –x+1 +4 +4 y = –x+5 y + 1 = – 1(x – 6) y+1=-x+6 -1 or -1 y =-x+5 2. ( – 1, – 2), (2, 7) ANSWER y + 2 = 3(x + 1) y + 2 = 3 x + 3 -2 or or -2 y = 3 x + 1 y – 7 = 3(x – 2) y – 7 = 3 x – 6 +7 or +7 y = 3 x + 1

5. 4 Write Linear Equations in Standard Form

Convert this equation into standard form: Ax + By = C 1. ) Multiply everything by 5 Move over the “x” term -2 x I CAN’T LEAD WITH A NEGATIVE!!! So let’s change the sign of each term. It’s kind of like moving backwards!

Convert this equation into standard form: Ax + By = C 2. ) +x +x Move over the “x” term

Convert this equation into standard form: Ax + By = C 3. ) Multiply everything by 2 Move over the “x” term + 1 x

Convert this equation into standard form: Ax + By = C 4. ) Multiply everything by 3 Move over the “x” term -2 x I CAN’T LEAD WITH A NEGATIVE!!! So let’s change the sign of each term.

Write an equation of the line in STANDARD FORM using the information given. 5. ) m = 2 and (3, -2) Start with Point-Slope Form Now put into slope-intercept form -2 -2 Now put into Standard form -2 x No LEADING NEGATIVES! Change all the signs of each term -2 x

Write an equation of the line in STANDARD FORM using the information given. 5. ) m = and (4, -5) Start with Point-Slope Form Now put into slope-intercept form Now put into Standard form Multiply everything by 2 No LEADING NEGATIVES! Change all the signs of each term -5 -5 - 3 x

Every one get communicators with a blank side!!!

Write an equation of the line in STANDARD FORM using the information given. 5. ) (-4, 4) and (0, 3) Start with Point-Slope Form Now put into slope-intercept form Now put into Standard form Multiply everything by 4 No LEADING NEGATIVES! Change all the signs of each term +4 +4 +1 x

Write the point-slope form of the line that passes through (4, 3) and (1, 2)

Write the slope-intercept form of the line that passes through (4, 5) and (1, -1)

Write an equation of the line in STANDARD FORM using the information given. 5. ) m = -2 and (-4, 3) Start with Point-Slope Form Now put into slope-intercept form +3 Now put into Standard form + 2 x +3

Write an equation of the line in STANDARD FORM using the information given. 5. ) m = -3 and (3, -5) Start with Point-Slope Form Now put into slope-intercept form Now put into Standard form Multiply everything by 2 No LEADING NEGATIVES! Change all the signs of each term -5 -5 - 3 x

Write an equation of the line in STANDARD FORM using the information given. 5. ) (4, 0) and (0, 3) Start with Point-Slope Form Now put into slope-intercept form Now put into Standard form Multiply everything by 4 + 3 x

Write an equation of the line in STANDARD FORM using the information given. 5. ) (2, 0) and (0, 5) Start with Point-Slope Form Now put into slope-intercept form Now put into Standard form Multiply everything by 2 + 5 x

EXAMPLE 2 Write an equation from a graph Write an equation in standard form of the line shown. SOLUTION STEP 1 Calculate the slope. 1 – (– 2) 3 m= = – 1 = – 3 1– 2 STEP 2 Write an equation in point-slope form. Use (1, 1). y – y 1 = m(x – x 1) Write point-slope form. y – 1 = – 3(x – 1) Substitute 1 for y 1, 3 for m and 1 for x 1.

EXAMPLE 2 Write an equation from a graph STEP 3 Rewrite the equation in standard form. 3 x + y = 4 Simplify. Collect variable terms on one side, constants on the other.

from 1 a and graph EXAMPLE 2 Write an equation for Examples 2 GUIDED PRACTICE 2. Write an equation in standard form of the line through (3, – 1) and (2, – 3). ANSWER – 2 x + y = – 7

EXAMPLE 4 3 Complete an equation in standard form Find the missing coefficient in the equation of the line shown. Write the completed equation. SOLUTION STEP 1 Find the value of A. Substitute the coordinates of the given point for x and y in the equation. Solve for A. Ax + 3 y = 2 A(– 1) + 3(0) = 2 –A = 2 A = – 2 Write equation. Substitute – 1 for x and 0 for y. Simplify. Divide by – 1.

EXAMPLE 4 Complete an equation in standard form STEP 2 Complete the equation. – 2 x + 3 y = 2 Substitute – 2 for A.

GUIDED PRACTICE for Examples 3 and 4 Write equations of the horizontal and vertical lines that pass through the given point. 3. (– 8, – 9) ANSWER y = – 9, x = – 8

GUIDED PRACTICE for Examples 3 and 4 Write equations of the horizontal and vertical lines that pass through the given point. 4. (13, – 5) ANSWER y = – 5, x = 13

Complete an equation standard form EXAMPLE 4 3 for Examples 3 in and 4 Write an equation of a line GUIDED PRACTICE Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation. 5. – 4 x + By = 7, (– 1, 1) ANSWER 3; – 4 x + 3 y = 7

EXAMPLE 1 Write equivalent equations in standard form Write two equations in standard form that are equivalent to 2 x – 6 y = 4. SOLUTION To write one equivalent equation, multiply each side by 2. 4 x – 12 y = 8 To write another equivalent equation, multiply each side by 0. 5. x – 3 y = 2

EXAMPLE 1 GUIDED PRACTICE for Examples 1 and 2 1. Write two equations in standard form that are equivalent to x – y = 3. ANSWER 2 x – 2 y = 6, 3 x – 3 y = 9

EXAMPLE 5 Solve a multi-step problem ANSWER The equation 8 s + 12 l = 144 models the possible combinations. b. Find the intercepts of the graph. Substitute 0 for s. 8(0) + 12 l = 144 l = 12 Substitute 0 for l. 8 s + 12(0) = 144 s = 18

Complete an equation standard form EXAMPLE 4 3 for Examples 3 in and 4 Write an equation of a line GUIDED PRACTICE Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation. 6. Ax + y = – 3, (2, 11) ANSWER – 7; – 7 x +y = – 3