Question

What is the equation of a line that is parallel to y=2x+5 and passes through (-6,4)?

a) y=2x-6
b) y=2x+16
c) y=2x+4
d) y=-1/2x+16

Answer 1

Let (D) which is y=ax+b

passes through (-6,4)

then substitute to get 4=-6a+b

we must find a and b

we have (D)// to y=2x+5 slope of (D) same as y=2x+5

then a=2

we get 4=-6*2+b i. e. b=16

so the correct answer is b which is y=2x+16

Answer 2

The line parallel to y=2x+5 that goes through the point (-6,4) is represented by the equation y=2x+16, obtained by using the point-slope form and the slope of 2 which is the same for parallel lines.

Step-by-step explanation:

The student's question asks for the equation of a line that is parallel to y=2x+5 and passes through the point (-6,4). Two lines are parallel when they have the same slope. Since the given line has a slope of 2, the parallel line must also have a slope of 2. We use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope.

Substituting the point (-6, 4) and slope 2 into the point-slope formula, we get:

y - 4 = 2(x + 6)
y - 4 = 2x + 12
y = 2x + 16

Therefore, the correct equation of the line parallel to y=2x+5 that passes through (-6,4) is y=2x+16.