Final answer:
The slope-intercept form of the equation that passes through the point (3,-4) and is parallel to the line y=3x+2 is y = 3x - 13.
Step-by-step explanation:
To determine the slope-intercept form of the equation that passes through the point (3,-4) and is parallel to the line y=3x+2, we need to use the fact that parallel lines have the same slope.
Given that the slope of the given line is 3, we can use the point-slope form of a linear equation to find the equation of the parallel line. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Substituting the values from the given point and the slope, we get y - (-4) = 3(x - 3), which simplifies to y + 4 = 3x - 9. Rearranging the equation in slope-intercept form gives us y = 3x - 13.