Point-Slope Form of a Line

Use the graph to find the x-intercept for the equation y + 2 = 2(x + 3). The x-intercept is ________________ (-2, 0) (0, 4) ( 2, 0) (4, 0)

A

Choose a linear function for the line represented by the point-slope equation y - 5 = 3(x - 2). f(x) = 3x + 1 f(x) = 3x - 1 f(x) = 8x + 10 f(x) = 8x - 10

B

A tile factory earns money by charging a flat fee for delivery and a sales price of $0.25 per tile. One customer paid a total of $3,000 for 10,000 tiles. The equation y - 3,000 = 0.25(x - 10,000) models the revenue of the tile factory, where x is the number of tiles and y is the total cost to the customer. Which function describes the revenue of the tile factory in terms of tiles sold? f(x) = 0.25x + 10,000 f(x) = 0.25x + 3,000 f(x) = 0.25x + 500 f(x) = 0.25x + 0.25 What is the flat fee for delivery? 0.25 500 3,000 10,000

1). C 2). B

What is the equation of the line in point-slope form? y + 4 = (x + 4) y - 4 = (x + 4) y - 0 = 2(x - 4) y - 4 = 2(x - 0)

A

Hugo decided to pay $2 a week to his brother to buy a bicycle. The equation y - 10 = -2(x - 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay. How much did the bicycle cost? $ 5 10 15 30 After how many weeks will Hugo finish paying for the bike? weeks 5 10 15 30

1). $30 2). 15 weeks

Use the point-slope equation to identify the slope and the coordinates of a point on the line y - 4 = (x - 1) The slope of the line is .________________ m= -2 m= -(1/2) m= 1/2 m = 2 A point on the line is ____________________ (-4,-1) (4, 1/2) (1/2, 1 (1,4)

1) C 2) D

Which point-slope equation represents a line that passes through (3, -2) with a slope of negative StartFraction 4 Over 5 EndFraction? y - 3 = -(x + 2) y - 2 = (x - 3) y + 2 = -(x - 3) y + 3 = (x + 2)

C

What is the y-intercept of the graphed linear function? (0, -8) (0, -2) (0, 2) (0, 4)

D

Use the graph of the line to answer the questions. What is an equation of the line in point-slope form? y - 1 = 3 (x + 0) y - 0 = 3 (x - 1) y + 1 = (1/3)(x+2) y+ 2 (1/3)(x+1) How can the point-slope form be written in function notation? f(x) = (1/3)x - (5/3) f(x) = (1/3)x - (1/3) f(x) = 3x - 3 f(x) + 3x + 1

Y = 1/3x - 1/3 Y + 1 = 1/3 (x + 2)

Which graph represents the function y - 3 = y minus 3 equals StartFraction 3 Over 2 EndFraction left-parenthesis x minus 4 right-parenthesis.(x - 4)?

A

Andy wrote the equation of a line that has a slope of StartFraction 3 Over 4 EndFraction and passes through the point (3, -2) in function notation. Step 1: y - (-2) = Step 1: y minus left-parenthesis negative 2 right-parenthesis equals StartFraction 3 Over 4 left-parenthesis x minus 3 right-parenthesis. (x - 3) Step 2: y + 2 = Step 2: y plus 2 equals StartFraction 3 Over 4 EndFraction x minus StartFraction 9 Over 4 EndFraction.x - Step 3: y + 2 + 2 = Step 3: y plus 2 plus 2 equals StartFraction 3 Over 4 x minus StartFraction 9 Over 4 EndFraction plus 2.x - + 2 Step 4: y = Step 4: y equals StartFraction 3 Over 4 EndFraction x minus StartFraction one-fourth.x - Step 5: f(x) = Step 5: f(x) equals StartFraction 3 Over 4 EndFraction x minus StartFraction one-fourth. x - nalyze each step to identify if Andy made an error. Yes, he made an error in Step 1. He switched the x and y values. Yes, he made an error in Step 2. He did not distribute StartFraction 3 Over 4 EndFraction properly. Yes, he made an error in Step 3. He should have subtracted 2 from both sides. No, his work is correct.

he made an error in Step 3. He should have subtracted 2 from both sides or C