Final answer:
The y-intercept of the line is -18.
Step-by-step explanation:
To find the y-intercept of a line passing through the point (3, -6) with a slope of 4, we can use the equation for a line: y = mx + b.
1. Substitute the given slope (m = 4) and the coordinates of the point (x = 3, y = -6) into the equation: -6 = 4(3) + b.
2. Simplify the equation: -6 = 12 + b.
3. To solve for b, subtract 12 from both sides of the equation: -6 - 12 = b, which gives us b = -18.
Therefore, the y-intercept of the line passing through the point (3, -6) with a slope of 4 is -18.
In this process, we used the equation of a line, y = mx + b, to substitute the given slope and point. By simplifying the equation and isolating the variable, we found the y-intercept of the line. Plugging in the values of the slope and the point allowed us to determine the value of the y-intercept, which is -18 in this case.