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.
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.
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