Point-Slope Form and Linear Equations Unit Test Review, Algebra, Unit Test Review, Unit Test Review

The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object's mass?

F = 32.2m

At a glance, Kendra believes that the function represented on the graph is linear. How can Kendra determine if the function is actually linear?

She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.

The pattern of numbers below is an arithmetic sequence: 14, 24, 34, 44, 54, ... Which statement describes the recursive function used to generate the sequence?

The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.

The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function?

The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.

Which statement best explains the relationship between lines PQ and RS?

They are not parallel because their slopes are not equal.

Which linear function is represented by the graph?

f(x) = -1/2x + 1

Which linear function represents the line given by the point-slope equation y + 7 = -(x + 6)?

f(x) = -2/3x -11

Which table represents a linear function?

x y 1 -2 2 -10 3 -18 4 -26

Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?

y - 1 = 3x

Which points lie on the line that passes through point P and is parallel to the given line? Check all that apply.

(-1, 3) (-2, 2) (-5, -1)

Which point is on the line that passes through point R and is perpendicular to line PQ?

(-4, -8)

To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?

-2/5

The table represents a linear function. x y What is the slope of the function? -4 -2 -2 -10 -1 -14 1 -22 2 -26

-4

Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

-9

Raphael graphed the functions g(x) = x + 2 and f(x) = x - 1. How many units below the y-intercept of g(x) is the y-intercept of f(x)?The y-intercept of f(x) is ____ units below the y-intercept of g(x).

3

The table represents a linear function. What is the slope of the function?

5

The table represents a linear function. x I y -4 I -16 -2 I -6 0 I 4 2 I 14 4 I 24

5

What is the constant of variation, k, of the line y = kx through (3,18) and (5,30)?

6

The table represents a linear equation. Which equation correctly uses point (-2, -6) to write the equation of this line in point-slope form?

y + 6 = 5/2(x + 2)

The table represents a linear equation. Which equation correctly uses point (-2, -6) to write the equation of this line in point-slope form?

y + 6 = 5/2(x + 2)

Mr. Shaw graphs the function f(x) = -5x + 2 for his class. The line contains the point (-2, 12). What is the point-slope form of the equation of the line he graphed?

y - 12 = -5(x + 2)

A line that passes through the points (-4, 10) and (-1, 5) can be represented by the equation y = (x - 2). Which equations also represent this line? Check all that apply.

y = -5/3x + 10/3 3y = -5x + 10 5x + 3y = 10

A line that passes through the points (-4, 10) and (-1, 5) can be represented by the equation y = -5/3(x - 2). Which equations also represent this line? Check all that apply.

y = -5/3x + 10/3 3y = -5x + 10 5x + 3y = 10

Which equation represents the graphed function?

y = 1/4x -2

A direct variation function contains the points (-8, -6) and (12, 9). Which equation represents the function?

y = 3/4x

What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)?

y = 3x − 5

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

y = 7x

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)?

y − 1 = −2(x − 4)

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)?

y − 5 = −(x − 2)

A direct variation function contains the points (-9, -3) and (-12, -4). Which equation represents the function?

y=x/3

What is the equation of the line that is parallel to the given line and passes through the point (2, 3)?

x + 2y = 8

What is the equation of the graphed line written in standard form?

x - 4y = 4

The points (3, 24) and (7, 56) represent points of a function where y, the number of photographs, varies directly with x, the number of pages in an album. Which statement describes another point on the graph of this function?

A 50-page photo album holds 400 photographs.

The graph of the equation x - 2y = 5 has an x-intercept of 5 and a slope of 1/2. Which shows the graph of this equation?

D

Which shows a graph of a linear equation in standard form Ax + By = C, where A = 0, B is positive, and C is negative?

D

A line is drawn through (-4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?

The line does not represent a direct variation because it does not go through the origin.

Timmy writes the equation f(x) = x - 1. He then doubles both of the terms on the right side to create the equation g(x) = x - 2. How does the graph of g(x) compare to the graph of f(x)?

The line of g(x) is steeper and has a lower y-intercept.

How does the slope of g(x) compare to the slope of f(x)?

The slope of g(x) is less than the slope of f(x).

Which is true of the standard form of the equation of the line graphed?

The value of A can only be 1, the value of C can only be -3, and the value of B is 0.

Which statement best explains the relationship between lines AB and CD?

They are parallel because their slopes are equal.

On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 2 when a = -2. Which equation represents this direct variation between a and b?

b = -a

Which linear function represents the line given by the point-slope equation y + 7 = -2/3(x + 6)?

f(x) = -2/3x - 11

Which linear function represents the line given by the point-slope equation y - 8 = 1/2(x - 4)?

f(x) = 1/2x + 6

Which linear function represents the line given by the point-slope equation y - 8 = (x - 4)?

f(x) = 1/2x -10

Mrs. Jackson gives the table below to her students. In order for the function to be linear, what must m be and why?

m = 20 because the rate of change is -3.

A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included tip for wait staff as a function of the number of guests served. CATERING COST FOR WAIT STAFF GRATUITY Number of guest Wait staff Tip 10 $18 20 $36 30 $54 40 $72 50 $90

t = 1.8g