...Find the point-slope form of the equation that passes through (-2, 4) and is parallel to the line given by y= -2x-10

y - 4 = -2(x + 2)

Step-by-step explanation:

Point-slope form: y - y1 = m(x - x1)

Point: (-2, 4) = (x1, y1)

Slope: unknown

To write the equation in point-slope form, we need to know the slope and one point. We know one point, but we still need to find the slope.

When two lines are parallel, their slopes are equal. The line y = -2x - 10 is in the form y = mx + b, where m is the slope. The slope of that line is -2, which means that the slope of the line parallel to it is also -2.

Now that we know the value of the slope and one point, we can write the equation in slope-intercept form:

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

y - 4 = -2(x + 2)

The equation in slope-intercept form is: y - 4 = -2(x + 2)