Daily Homework Quiz Review 5.3 Write an equation in point-slope form of the line that passes through (6, –4) and has slope 2. 1. y – y1 = m(x – x1) ANSWER y + 4 = 2(x – 6) Write an equation in point-slope form of the line that passes through (–1, –6) and (3, 10). 2. 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) 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 2. ( –1, –2), (2, 7) ANSWER y + 2 = 3(x + 1) or y – 7 = 3(x – 2) y + 2 = 3x + 3 or y – 7 = 3x – 6 - 2 - 2 + 7 + 7 y = 3x + 1 or y = 3x + 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 -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!

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 + 1x + 1x

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.

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

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

Every one get communicators with a blank side!!!

Write an equation of the line in STANDARD FORM using the information given. 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

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

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

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

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

Write an equation from a graph EXAMPLE 2 Write an equation from a graph Write an equation in standard form of the line shown. SOLUTION STEP 1 Calculate the slope. –3 m = 1 – (–2) 1 – 2 = 3 –1 STEP 2 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.

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

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

Complete an equation in standard form EXAMPLE 3 EXAMPLE 4 EXAMPLE 4 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 + 3y = 2 Write equation. A(–1) + 3(0) = 2 Substitute –1 for x and 0 for y. –A = 2 Simplify. A = –2 Divide by –1.

Complete an equation in standard form EXAMPLE 4 Complete an equation in standard form STEP 2 Complete the equation. –2x + 3y = 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) y = –9, x = –8 ANSWER

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

EXAMPLE 4 EXAMPLE 3 Complete an equation in standard form GUIDED PRACTICE Write an equation of a line for Examples 3 and 4 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) ANSWER 3; –4x + 3y = 7

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

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

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

EXAMPLE 4 EXAMPLE 3 Complete an equation in standard form GUIDED PRACTICE Write an equation of a line for Examples 3 and 4 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; –7x +y = –3