Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.(2-2);y=-x-2 (1 point) Responses Image with alt text: y equals negative 2 x. Image with alt text: y equals 2 x. Image with alt text: y equals one-half x.
To find the equation of a line that is parallel to the given equation, we note that parallel lines have the same slope. The given equation is y = -x - 2, which has a slope of -1.
Since the parallel line has the same slope, its equation will also have a slope of -1. Now we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Using the point (2, -2) and slope -1, the equation becomes:
y - (-2) = -1(x - 2)
y + 2 = -x + 2
Finally, rearranging the equation into slope-intercept form (y = mx + b), we get:
y = -x + (2 - 2)
y = -x + 0
Thus, the equation of the line passing through the given point and is parallel to the graph of y = -x - 2 is y = -x.