Final answer:
The y-intercept of a line with a slope of -3 that passes through the point (12,2) is calculated using the equation y = mx + b, which results in a y-intercept of 38. The line crosses the y-axis at the point (0, 38).
Step-by-step explanation:
The student has asked to find the y-intercept of a line with a slope of -3 that passes through the point (12,2). To find the y-intercept, we can use the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Since we know the slope (m) is -3 and the line passes through the point (12,2), we can substitute these values into the equation to solve for b.
- First, substitute the point into the equation: 2 = (-3)(12) + b.
- Solve for b: 2 = -36 + b.
- Add 36 to both sides: b = 2 + 36 = 38.
Therefore, the y-intercept of the line is b = 38, meaning the line crosses the y-axis at the point (0, 38).