Find the slope-intercept form of the line passing through the point (-3, -6) and parallel to the line y = 5x + 4.

Sure, here are the steps to find the slope-intercept form of the line:

Step 1: Identify the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. For the line y = 5x + 4, the slope is 5.

Step 2: Use the slope of the parallel line. Lines that are parallel have the same slope. Therefore, the slope of the line we are trying to find is also 5.

Step 3: Use the point-slope form of a line. The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We know that the line passes through the point (-3, -6) and has a slope of 5, so we can substitute these values into the equation to get y - (-6) = 5(x - (-3)).

Step 4: Simplify the equation. Simplify the equation from step 3 to get y + 6 = 5(x + 3).

Step 5: Distribute the 5 on the right side of the equation. This gives us y + 6 = 5x + 15.

Step 6: Subtract 6 from both sides to get the equation in slope-intercept form. This gives us the final equation of the line: y = 5x + 9.