Question

Calvin states that it is not possible to find the equation of a line parallel to y=2

and passing through the point (5,−1)
using the point-slope form because the equation of the line does not have an x-term.

Find the equation of the parallel line through the given point.

Answer 1

y = -1

Explanation:

Calvin's statement is not accurate. We can indeed find the equation of a line parallel to y=2 and passing through the point (5,-1) using the point-slope form.

The equation of a line in point-slope form is given by y - y1 = m(x - x1), where (x1, y1) represents a point on the line and m represents the slope of the line.

In this case, the given line y = 2 has a slope of 0, as there is no x-term. Since we want to find a parallel line, it will also have a slope of 0.

Using the point-slope form, we substitute the values of the given point (5, -1) and the slope 0 into the equation:

y - (-1) = 0(x - 5)

Simplifying the equation, we have:

y + 1 = 0

To write the equation in standard form, we can move the y term to the other side of the equation:

y = -1

Therefore, the equation of the parallel line through the point (5, -1) is y = -1.