Parallel and Perpendicular Lines
Two lines that are parallel have the same...?
Slope.
What is the equation of a line written in slope-intercept form?
y = mx + b
What is the equation of a line written in standard form?
Ax + By = C
What is the equation of a line written in standard form?
y-y1=m(x-x1)?
Yuson must complete a certain number of hours of community service. She does 2 hours of service each day. After 8 days, Yuson has completed half of her required community service.
If you graphed an equation based on this information, what would the y-intercept represent?
The total number of hours of community service.
Two lines that are perpendicular have _____ slopes.
Negative reciprocal.
e.g. 4/5 and -5/4.
What is the slope-intercept form equation of a line with a slope of 3 and a y-intercept at (0, 13)?
y = 3x + 13
The number C in a standard form equation is called the...?
Constraint.
Unlike equations written in slope-intercept form, linear equations written in point-slope form do not need a...?
y-intercept.
Graph the line x = 3.
Write the slope of a line that is perpendicular to y = 3x - 4.
m = -1/3
What is the slope of a line that passes through the points (2, 9) and (-1, 3)?
2
Malik will spend $150 dollars on concert tickets for his group of friends. Reserved seat tickets cost $25 and normal tickets cost $10. Write a standard form equation to represent this situation.
25x + 10y = 150
What is the point-slope form equation of a line with a slope of 4 and a point at (3, 7)?
y - 7 = 4(x - 3)
Convert 18x - 3y = 15 to slope-intercept form.
y = -5 + 6x
Write an equation of a line that is perpendicular to the line y = (3/4)x + 12 and passes through the point (3, 1).
y = -(4/3)x + 5
Shauna was given $100 dollars for her 18th birthday. She uses that money to pay for Spotify Premium, which costs about $10 per month. Write a linear equation to represent how much money Shauna has left after x months of paying for Spotify Premium.
y = -10x + 100
Colin is buying food for a birthday party. His budget is $60 dollars. He can buy a box of cookies, x, for $15. He can buy a giant bag of chips, y, for $12 dollars. If he buys three bags of chips, how many boxes of cookies can he buy without going over his budget? Write and solve a standard form equation to support your answer.
The equation is 15x + 12y = 60.
If Colin buys 3 bags of chips, he can buy 1 box of cookies.
15x + 12(3) = 60
15x + 36 = 60
15x = 24
x = 1.6
Convert the following point-slope equation to slope-intercept form:
y + 4 = -3(x - 1)
y = -3x - 1
What are the x- and y-intercepts of this line?
2x + 4y = 20
y-intercept is (0, 5). x-intercept is (10, 0).
Write the equation of the line that is parallel to y = (1/2)x + 3 and passes through the point (-1, 5).
y = (1/2)x + 5.5
Marcus has a gift card for a local cupcake shop. After buying two cupcakes, Marcus had $19.70 left on the card. After buying four cupcakes, Marcus had $14.40 left on the card. How much money was originally on the card?
$25.00
What does the graph of a standard form equation look like if A = 0 and B =/= 0?
The graph would be a horizontal line.
e.g. 0x + 3y = 12
3y = 12
y = 4
y = 4 is a horizontal line.
Maya wants to rent a banquet hall for a wedding party. The cost to rent a certain banquet hall for 50 people is $725. The cost to rent the same hall for 150 people is $1,925. Maya's budget is $1,200 dollars. If Maya wants to rent the banquet hall for 75 people, does she have enough money? Write an equation in point-slope form and solve it to get your answer. (# of guests is on the x-axis, and cost is on the y-axis).
The equation is y - 725 = 12(x - 50). The equation y - 1925 = 12(x - 150) would also work.
The answer is that Maya does have enough money. When x = 75, y = 1,025, which is less than Maya's budget.
What is the slope of this line?
4x + 2y = 10
-2