A line, y = mx + b, passes through the point (1,6) and is parallel to y=4x+6. What is the value of b?
B=2
To find the value of b in the equation y = mx + b for a line that is parallel to y = 4x + 6 and passes through the point (1,6), we can use the fact that parallel lines have the same slope.
The given line y = 4x + 6 is in slope-intercept form, where the slope (m) is the coefficient of x. In this case, the slope is 4.
Since the parallel line has the same slope, our new line also has a slope of 4.
Now we can substitute the slope and the coordinates of the point (1,6) into the equation y = mx + b.
Using the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line, we have:
y - 6 = 4(x - 1)
Next, we distribute the 4 into the parentheses:
y - 6 = 4x - 4
Move the 4x term to the left side by subtracting 4x from both sides:
-4x + y - 6 = -4
Now, isolate y by moving the constant term to the right side:
y = -4 + 6
Simplifying the equation gives:
y = 2
So the value of b is 2.
To find the value of b, we need to use the fact that the line we are looking for is parallel to the given line y = 4x + 6.
The equation of a line parallel to y = mx + b will have the same slope as the given line, but a different y-intercept.
Given that the slope of the given line is 4, the equation of the parallel line is y = 4x + b.
To find the value of b, we can use the fact that the line passes through the point (1,6). This means that when x = 1, y = 6.
Substituting these values into the equation of the line, we have:
6 = 4(1) + b
Simplifying the equation, we get:
6 = 4 + b
To isolate b, we subtract 4 from both sides:
6 - 4 = b
2 = b
Therefore, the value of b is 2.
parallel means the lines have the same slope ... their m's are equal
y = 4 x + b ... through (1,6)
plug in the point , and solve for b
... y = 6 , and x = 1