Write the equation of the line that passes through the point P (1, -2) and is parallel to the line shown in the diagram below.

1 answer

To find the equation of a line parallel to another line, we need to determine the slope of the given line. From the diagram, we can see that the given line has a slope of 2.

Since the parallel line has the same slope, we know that the slope of the parallel line is also 2.

The equation of a line can be determined using the point-slope formula: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.

Using the given point P(1, -2) and the slope m = 2, we can substitute these values into the equation:

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

Simplifying the equation:

y + 2 = 2(x - 1)

Distributing the 2 on the right side:

y + 2 = 2x - 2

Subtract 2x from both sides:

y + 2x + 2 = 0

Rearranging the equation to slope-intercept form:

y = -2x -2

Thus, the equation of the line passing through point P(1, -2) and parallel to the given line is y = -2x - 2.