Question

Write an equation of a line that passes through (-4, 4) and is parallel to the line y=1/2x+1

Answer 1

Therefore, the equation of the line that passes through (-4, 4) and is parallel to the line y = (1/2)x + 1 is y = (1/2)x + 6.

Explanation:

To find the equation of a line that is parallel to the line y = (1/2)x + 1 and passes through the point (-4, 4), we need to use the fact that parallel lines have the same slope.

The given line has a slope of 1/2, so the parallel line we want to find must also have a slope of 1/2.

We can use the point-slope form of the equation of a line to write the equation of the parallel line. The point-slope form is:

y - y1 = m(x - x1)

where (x1, y1) is the given point on the line, and m is the slope of the line.

Substituting the values we have:

m = 1/2 (the slope of the parallel line)

x1 = -4

y1 = 4

So the equation of the parallel line is:

y - 4 = (1/2)(x - (-4))

Simplifying this equation gives:

y - 4 = (1/2)x + 2

Adding 4 to both sides gives:

y = (1/2)x + 6

Therefore, the equation of the line that passes through (-4, 4) and is parallel to the line y = (1/2)x + 1 is y = (1/2)x + 6.

Answer 2

y = 1/2x + 6

Explanation:

Two lines are parallel if they have the same slope. The slope of the given line y = 1/2x + 1 is 1/2. So the slope of the line that passes through (-4, 4) and is parallel to the given line is also 1/2.

We can use point-slope form to write the equation of the new line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting in the point (-4, 4) and the slope 1/2, we get: y - 4 = 1/2(x + 4).

Simplifying this equation gives us y = 1/2x + 6. So the equation of the line that passes through (-4, 4) and is parallel to the line y = 1/2x + 1 is y = 1/2x + 6.