Question

Write the equation of the line which passes through (–4, 2) and is parallel to y = –x + 6 in slope-intercept form.

Answer 1

y=-x -2

Answer 2

y = -x+6 has a slope of -1 since it's in the form y = mx+b (and m is the slope)


ANY parallel line to this line will have a slope of -1 also


So the equation of this unknown parallel line is

y = -x+b


but since this line passes through (-4,2), we know that x = -4 and y = 2


So


2 = -(-4) + b

2 = 4 + b

2-4 = b

-2 = b

b = -2


So the equation of the parallel line that passes through (-4,2) is y = -x-2

Answer 3

Write the equation of the line which passes through (2, –3) and is perpendicular to y = 4x + 7 in standard form.

Answer 4

With perpendicular lines, the slopes are negative reciprocals of each other.


So here the given slope is 4, which means that the perpendicular slope will be -1/4 (flip the fraction and the sign)


So the perpendicular equation will look like


\[\large y = -\frac{1}{4}x+b\]


Use the fact that the line passes through (2,-3) and plug in x=2 and y = -3 into the equation above to solve for 'b' to get your answer

Answer 5

Graciiiiiias