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ANSWER

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

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  1. 1. Write an equation in point-slope form of the line that passes through (6, –4) and has slope 2. ANSWER y + 4 = 2(x – 6) 2. Write an equation in point-slope form of the line that passes through (–1, –6) and (3, 10). y + 6 = 4(x + 1) ory –10 = 4(x–3) ANSWER Daily Homework Quiz Review 5.3 y –y1=m(x –x1)

  2. Review 5.3 2. ( –1, –2), (2, 7) Write an equation in point-slope form of the line that passes through the given points. 1. (1, 4), (6, –1) NOW PUT EACH ANSWER IN SLOPE-INTERCEPT FORM!! ANSWER y – 4 = –1(x – 1) or y + 1 = –1(x – 6) y – 4 = – x + 1 or y + 1 = - x + 6 + 4 + 4 - 1 - 1 y = – x + 5 or y = - x + 5 ANSWER y + 2 = 3(x + 1) ory– 7 = 3(x– 2) y + 2 = 3x + 3 ory– 7 = 3x– 6 - 2 - 2 + 7 + 7 y = 3x + 1 or y = 3x + 1

  3. 5.4 Write Linear Equations in Standard Form

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

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

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

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

  8. 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 -2x -2x No LEADING NEGATIVES! Change all the signs of each term

  9. 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 - 5 - 5 Now put into Standard form Multiply everything by 2 - 3x - 3x No LEADING NEGATIVES! Change all the signs of each term

  10. Every one get communicators with a blank side!!!

  11. 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 + 4 + 4 Now put into Standard form Multiply everything by 4 +1x +1x No LEADING NEGATIVES! Change all the signs of each term

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

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

  14. 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 + 3 Now put into Standard form + 2x + 2x

  15. 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 - 5 - 5 Now put into Standard form Multiply everything by 2 - 3x - 3x No LEADING NEGATIVES! Change all the signs of each term

  16. 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 + 3x + 3x

  17. 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 + 5x + 5x

  18. 1 – (–2) m= –3 = = 1 – 2 3 –1 Write an equation from a graph EXAMPLE 2 Write an equation in standard form of the line shown. SOLUTION STEP1 Calculate the slope. STEP2 Write an equation in point-slope form. Use (1, 1). y –y1=m(x –x1) Write point-slope form. y –1=–3(x –1) Substitute 1 for y1, 3 for m and 1 for x1.

  19. Write an equation from a graph EXAMPLE 2 STEP3 Rewrite the equation in standard form. 3x + y = 4 Simplify. Collect variable terms on one side, constants on the other.

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

  21. Find the missing coefficient in the equation of the line shown. Write the completed equation. Complete an equation in standard form EXAMPLE 4 EXAMPLE 3 EXAMPLE 4 SOLUTION STEP1 Find the value of A. Substitute the coordinates of the given point for xandyin the equation. Solve forA. Ax + 3y = 2 Write equation. A(–1) + 3(0) = 2 Substitute –1 for x and 0 for y. Simplify. –A = 2 A = –2 Divide by –1.

  22. Complete an equation in standard form EXAMPLE 4 STEP2 Complete the equation. –2x + 3y = 2 Substitute –2 for A.

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

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

  25. ANSWER 3; –4x + 3y = 7 Complete an equation in standard form EXAMPLE 4 EXAMPLE 3 for Examples 3 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. –4x + By = 7, (–1, 1)

  26. EXAMPLE 1 Write equivalent equations in standard form Write two equations in standard form that are equivalent to 2x – 6y =4. SOLUTION To write another equivalent equation, multiply each side by 0.5. To write one equivalent equation, multiply each side by 2. 4x – 12y =8 x – 3y = 2

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

  28. ANSWER The equation 8s+12l=144 models the possible combinations. Solve a multi-step problem EXAMPLE 5 b. Find the intercepts of the graph. Substitute0fors. 8(0) + 12l = 144 l = 12 Substitute 0 for l. 8s + 12(0) = 144 s = 18

  29. ANSWER –7; –7x +y = –3 Complete an equation in standard form EXAMPLE 4 EXAMPLE 3 for Examples 3 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)

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