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Lindsay used two points, (x 1, y 1) and (x 2, y 2), to find the equation of the line, y = mx + b, that passes through the points. First, she used the definition of slope and determined that the value of m is StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. Given this information, which expression must represent the value of b?
y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
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which onw is the awnser i did not understand

A)y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
B)y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
C)y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
D)y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
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What can be concluded about the line represented in the table? Select 3 options.

x
y
–6
–7
2
–3
8
0

The slope is 2.
The slope is One-half.
The y-intercept is –4.
The y-intercept is 8.
The points (–2, –5) and (8, 0) are also on the line.
The points (–5, –2) and (1, 10) are also on the line.
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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
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What is the equation of the linear function represented by the table?

x
y
–5
14
–2
11
1
8
4
5
y = negative x + 9
y = negative x + 13
y = x + 13
y = x + 9
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The cost for a different taxi company is expressed with the equation y = 1.65x + 2.35, where x represents the miles driven and y represents the cost per trip. If Susan takes a taxi for the 14-mile trip from the bus terminal to her house, how much will the ride cost?

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The correct expression for the value of b is:

y 1 - (StartFraction y 2 - y 1 Over x 2 - x 1 EndFraction) (x 1)

This is because the equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). To find the value of b, we can use one of the points that the line passes through. Let's use (x1, y1):

y1 = mx1 + b

To isolate b, we can subtract mx1 from both sides:

y1 - mx1 = b

Now we just need to substitute the value of m that we were given:

y1 - (StartFraction y 2 - y 1 Over x 2 - x 1 EndFraction) (x 1) = b

And that's our answer!
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The answer is:

y 1 - (StartFraction y 2 - y 1 Over x 2 - x 1 EndFraction) (x 1)

Choice A.
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The following can be concluded about the line represented in the table:

- The slope is One-half.
- The y-intercept is 8.
- The points (–2, –5) and (8, 0) are also on the line.
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The equation of the line in slope-intercept form is:

y = 2x + 8

Choice B.
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The equation of the linear function represented by the table is:

y = -x + 9

Choice A.
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We are given the equation:

y = 1.65x + 2.35

where x represents the miles driven and y represents the cost per trip.

We know that Susan is taking a 14-mile trip, so we need to substitute 14 for x in the equation and solve for y:

y = 1.65(14) + 2.35
y = 23.1 + 2.35
y = 25.45

Therefore, the cost of the 14-mile taxi ride will be $25.45.

Answer: $25.45.