Aiko types at a rate of 50 words per minute. After typing at the same rate for 3 minutes, he has typed a total of 150 words.
This situation can be represented with a linear equation written in point-slope form, where x represents the number of minutes and y represents the number of words.
Use this information to complete each statement about the linear equation.
1. The slope of the linear equation is _.
2. One point on the graph of the linear equation will be _.
A. (3, 50)
B. (3, 150)
C. (50, 3)
D. (50, 150)
3. This linear equation can be written as _.
A. y - 150 = 50(x - 3)
B. y - 50 = 3(x - 150)
C. y - 3 = 150(x - 50)
1. The slope of the linear equation is 50.
2. One point on the graph of the linear equation will be B. (3, 150)
3. This linear equation can be written as A. y - 150 = 50(x - 3)
The graphed line: (0, -1), (-1, -3) The graphed line can be expressed by which equation?
A. y - 0 = 2(x + 1)
B. y + 3 = 2(x + 1)
C. y + 1 = -2(x - 0)
D. y - 3 = 2(x - 1)
The slope of the line can be calculated by using the points (0, -1) and (-1, -3) as follows:
Slope = (y2 - y1) / (x2 - x1)
Slope = (-3 - (-1)) / (-1 - 0)
Slope = (-3 + 1) / (-1)
Slope = -2 / -1
Slope = 2
The slope of the line is 2. Now, using the point-slope form of the equation y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line, we can substitute the values into the equation:
Using point (0, -1):
y - (-1) = 2(x - 0)
y + 1 = 2x
y = 2x - 1
Therefore, the correct equation for the graphed line is: y = 2x - 1
Among the options provided,
A. y - 0 = 2(x + 1) does not match the equation found.
B. y + 3 = 2(x + 1) does not match the equation found.
C. y + 1 = -2(x - 0) does not match the equation found.
D. y - 3 = 2(x - 1) matches the equation found.
So, the correct answer is D. y - 3 = 2(x - 1).
D is actually incorrect. Try again...
I apologize for the mistake. Let's reevaluate the options:
The correct equation for the graphed line based on the points (0, -1) and (-1, -3) is y = 2x - 1.
Among the options provided:
A. y - 0 = 2(x + 1) simplifies to y = 2x + 2 which does not match the equation found.
B. y + 3 = 2(x + 1) simplifies to y = 2x - 1 after working through the equation.
C. y + 1 = -2(x - 0) simplifies to y = -2x - 1 which does not match the equation found.
D. y - 3 = 2(x - 1) simplifies to y = 2x - 1 after working through the equation.
After reevaluation, it appears that both options B and D provide the correct equation for the graphed line. Therefore, the correct answer is both B. y + 3 = 2(x + 1) and D. y - 3 = 2(x - 1).