Final answer:
To find an equation in slope-intercept form that is parallel to y = -2x + 5 and passes through the point (1, -4), use the point-slope form of a linear equation and the fact that parallel lines have the same slope. The resulting equation is y = -2x - 2.
Step-by-step explanation:
To find an equation in slope-intercept form that is parallel to y = -2x + 5 and passes through the point (1, -4), we need to use the fact that parallel lines have the same slope. The given line has a slope of -2, so the parallel line will also have a slope of -2.
Using the point-slope form of a linear equation, we can plug in the values of the point and slope into the equation: y - y1 = m(x - x1) where (x1, y1) is the given point and m is the slope.
Substituting the values, we get y - (-4) = -2(x - 1). Simplifying this equation gives us y + 4 = -2x + 2. To write it in slope-intercept form, we isolate y by subtracting 4 from both sides: y = -2x - 2.