Final answer:
The equation in slope-intercept form of the line parallel to y = x + 36 and passes through the point (6, -12) is y = x - 18.
None of the given options is correct
Step-by-step explanation:
The equation in slope-intercept form of a line is y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To find the equation of the line that is parallel to the line y = x + 36 and passes through the point (6, -12), we need to determine the slope of the given line.
The slope of the line y = x + 36 is 1, as the coefficient of x is 1.
Since the line we are looking for is parallel to this line, it will also have a slope of 1.
Now that we have the slope (m = 1), we can substitute the given point (6, -12) and the slope (1) into the slope-intercept form equation to find the y-intercept (b).
Using the point-slope formula: y - y1 = m(x - x1), we substitute the values:
y - (-12) = 1(x - 6)
y + 12 = x - 6
Next, we isolate y to get it in the form y = mx + b:
y = x - 6 - 12
y = x - 18
Therefore, the equation in slope-intercept form of the line that passes through the point (6, -12) and is parallel to the line y = x + 36 is y = x - 18.
None of the answer choices provided match the correct equation, so the correct answer is none of the above.
Your question is incomplete, but most probably the full question was:
What is the equation in slope-intercept form of the line that passes through the point (6, -12) and is parallel to the line represented by y = x + 36 ?
F. y = -x - 16
G. y = x + 16
H. y = -x + 21
I. y = x + 21
J. y= x - 30
K. y=-x- 21