Final answer:
The equation of a line with a slope of -3 that passes through the point (7, -17) can be written in slope-intercept form as y = -3x + 4. The y-intercept of this line is the point (0, 4).
Step-by-step explanation:
To write the equation of a line with a slope of -3 that passes through the point (7, -17), we can use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in our values, we get y + 17 = -3(x - 7). To put this equation into slope-intercept form, which is y = mx + b, we distribute and simplify to get y = -3x + 21 - 17, which simplifies further to y = -3x + 4.
The y-intercept of this equation is when x = 0, which gives us y = 4. So the line crosses the y-axis at the point (0, 4). The intercept form of a line is not typically used, as it is generally reserved for hyperbolas, but the closest equivalent for a line would involve setting the equation into a format emphasizing the intercepts, such as x/(-4/3) + y/4 = 1. However, the slope-intercept form is more commonly used for lines, which in this case, is already given by y = -3x + 4.