A line, y = mx + b, passes through the point (1,6) and is parallel to y=4x+ 6. What is the value of b?
1.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
To find the value of b, we need to use the fact that the given line is parallel to another line. When two lines are parallel, they have the same slope.
In the given equation, y=4x+6, the slope is 4. So, the parallel line will also have a slope of 4.
Now, we can use the point-slope form of a linear equation to find the equation of our parallel line. The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the values, we have:
y - 6 = 4(x - 1)
Expanding the equation, we get:
y - 6 = 4x - 4
Now, rearrange the equation to isolate y:
y = 4x - 4 + 6
y = 4x + 2
Comparing this equation with the given line, y = mx + b, we can see that the slope (m) is the same (4).
Since both lines are parallel, they will never intersect and will have the same slope. Therefore, the value of b remains the same.
Thus, the value of b for the line y = 4x + 2 is also 2.