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)
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!
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)
The answer is:
y 1 - (StartFraction y 2 - y 1 Over x 2 - x 1 EndFraction) (x 1)
Choice A.
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.
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.
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
The equation of the line in slope-intercept form is:
y = 2x + 8
Choice B.
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
The equation of the linear function represented by the table is:
y = -x + 9
Choice A.