Asked by zach

A linear function has an x-intercept of 12 and a slope of StartFraction 3 Over 8 EndFraction. How does this function compare to the linear function that is represented by the table?

x
y
Negative two-thirds
Negative three-fourths
Negative one-sixth
Negative StartFraction 9 Over 16 EndFraction
One-third
Negative StartFraction 3 Over 8 EndFraction
StartFraction 5 Over 6 EndFraction
Negative StartFraction 3 Over 16 EndFraction
It has the same slope and the same y-intercept.
It has the same slope and a different y-intercept.
It has the same y-intercept and a different slope.
It has a different slope and a different y-intercept.
Answered by zach
What are the slope and the y-intercept of the linear function that is represented by the table?

x
y
–3
18
0
12
3
6
6
0

The slope is –2, and the y-intercept is 6.
The slope is –2, and the y-intercept is 12.
The slope is 2, and the y-intercept is 6.
The slope is 2, and the y-intercept is 12.
Answered by zach
Which is a characteristic of the line that passes through the points (6, 10) and (12, 7)?
The slope is One-half.
The slope is Negative 2.
The y-intercept is 7.
The y-intercept is 13.
Answered by zach
The value of a collectible coin can be represented by the equation y = 2 x + 9.74, where x represents the number of years that Consuello has owned the coin and y represents the total value, in dollars, of the coin. What was the value of the coin when Consuello originally purchased it?
$4.87
$7.74
$9.74
$19.48
Answered by zach
What are the slope and the y-intercept of the linear function that is represented by the graph?

On a coordinate plane, a line goes through points (0, negative 2) and (3, 0).
The slope is Two-thirds, and the y-intercept is –2.
The slope is Two-thirds, and the y-intercept is 3.
The slope is Three-halves, and the y-intercept is –2.
The slope is Three-halves, and the y-intercept is 3.
Answered by zach
The graph shows the number of hours that Tammy spends typing for work, x, and the amount of pay that she earns, y.

On a graph titled Tammy's Pay, number of hours is on the x-axis and pay in dollars is on the y-axis. A line goes through points (2, 18) and (8, 42).

What is the slope of the line?
One-fourth
StartFraction 8 Over 17 EndFraction
4
6
Answered by zach
Misty correctly determined the equation of the linear function represented by the table of values below to be y = negative 2 x + 9 in slope-intercept form by using the ordered pairs (1, 7) and (2, 5).

x
y
1
7
2
5
3
3
4
1

What would she have gotten for the equation of the linear function if she had used the ordered pairs (2, 5) and (4, 1) instead?
y = negative 4 x + 9
y = negative 4 x + 18
y = negative 2 x + 9
y = negative 2 x + 18
Answered by zach
Mike correctly found the slope and y-intercept of the line passing through the points (–5, –2) and (3, 14) as follows.

m = StartFraction 14 minus (negative 2) Over 3 minus (negative 5) EndFraction = StartFraction 16 Over 8 EndFraction = 2. y = 2 x + b. Negative 2 = 2 (negative 5) + b. Negative 2 + 10 = negative 10 + b + 10. b = 8.


What is the equation of the line in slope-intercept form?
y = 2 x minus 8
y = 2 x + 8
y = 8 x minus 2
y = 8 x + 2
Answered by zach
What method can be used to write the equation of a line in slope-intercept form given two points?
Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
Answered by zach
Consider the linear function that is represented by the equation y = 2 x + 2 and the linear function that is represented by the graph below.

On a coordinate plane, a line goes through points (negative 1, negative 1) and (0, 1).

Which statement is correct regarding their slopes and y-intercepts?
The function that is represented by the equation has a steeper slope and a greater y-intercept.
The function that is represented by the equation has a steeper slope, and the function that is represented by the graph has a greater y-intercept.
The function that is represented by the graph has a steeper slope, and the function that is represented by the equation has a greater y-intercept.
The function that is represented by the graph has a steeper slope and a greater y-intercept.
Answered by zach
Lila wrote an equation of the cost for printing brochures, where x represents the number of brochures and y represents the total cost. The total cost for 35 brochures is $41.45. The total cost for 65 brochures is $55.55.

Step 1: Write the ordered pairs (35, 41.45) and (65, 55.55).

Step 2: Find the slope. m = StartFraction 55.55 minus 41.45 Over 65 minus 35 EndFraction = 0.47

Step 3: Find the y-intercept to write the equation in slope intercept form. y minus 55.55 = 0.47 (x minus 35). Y minus 55.55 = 0.47 x minus 16.45. y = 0.47 x + 39.1.

Which explains the error that Lila made?
Lila made in error in Step 1 by reversing the ordered pairs.
Lila made an error in Step 2 by not using the slope formula.
Lila made an error in Step 3 when she did not use the x- and y-coordinates from the same ordered pair.
Lila made an error in Step 3 when she did not use the distributive property correctly when multiplying.
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