write an equation for the line that is parallel to the given line and passes through the given point. y=2x+4: (3,8)
A. y=2x+2
B. y=2x+6
C. y=-2x+6
D. y=-1/2+2
The form is y = m x + b
m is the slope
b is the y axis intercept, where the line hits the y axis when x = 0
so
the slope here is m = 2
and the line will look like
y = 2 x + b
so it is not C and it is not D
now
what happens when x = 3?
y = 2(3) + b = 6+b
but y better be 8
so b must be 2
so we end up with A
y = 2 x + 2
Thank you!
To find the equation of a line that is parallel to the given line and passes through the given point (3, 8), we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, we identify the slope of the given line. The given line has the equation y = 2x + 4, which means the slope (m) is 2.
Since the line we're looking for is parallel to the given line, it will have the same slope of 2.
Now, substitute the point (3, 8) into the equation y = mx + b to find the value of b.
8 = (2)(3) + b
8 = 6 + b
b = 2
Now that we have the slope (m = 2) and the y-intercept (b = 2), we can write the equation of the line:
y = 2x + 2
Therefore, the correct answer is:
A. y = 2x + 2