A line, y = mx + b, passes through the point (1,6) and is parallel to y=4x+ 6. What is the value of b?
2. The table below shows the hours, x, spent working on a new road and the distance, y, of finished road.
Time (hours) Distance (miles)
50 1.5
200 6
350 10.5
400 12
650 19.5
What is the slope of the line that fits these data points?
A. 3400
B. 3100
C. 335
D. 3
There is a space between the time and distance, I put them differently, and when I submitted the question, they posted as that. Sorry! For any confusion!
#1, Since the new line is to be parallel to the given line, it must also have a slope of 4
So it must look like y = 4x + b
sub in your given point, find b, and rewrite my equation.
#2. None of the given choices make sense for your given data
the slope between any two points in the given data is .03
thank you!
1. To find the value of b for a line parallel to y = 4x + 6, we need to use the fact that parallel lines have the same slope. In this case, the slope, m, of the line y = 4x + 6 is 4.
We also know that the line passes through the point (1, 6).
Using the point-slope form of a line, we can substitute the values into the equation:
y - y1 = m(x - x1)
where (x1, y1) is the point (1, 6).
Substituting the values, we get:
y - 6 = 4(x - 1)
Expanding the equation gives:
y - 6 = 4x - 4
Now, rearrange the equation to solve for y:
y = 4x + 2
Comparing this equation to the general form of a line, y = mx + b, we see that the value of b is 2.
Therefore, the value of b for the line parallel to y = 4x + 6 passing through the point (1, 6) is 2.
2. To find the slope of the line that fits the data points in the table, we can use the formula for slope:
slope = (change in y) / (change in x)
We can choose any two points from the table to calculate the slope.
Let's choose the points (50, 1.5) and (200, 6) in the table.
The change in y is:
6 - 1.5 = 4.5
The change in x is:
200 - 50 = 150
Using the slope formula, we obtain:
slope = 4.5 / 150 = 0.03
So, the slope of the line that fits the data points is 0.03.
None of the answer options provided match this value, so none of the answer options are correct.