Final answer:
The y-intercept of the line y = 6x + 13 is the point (0, 13), and the x-intercept is the point (-13/6, 0). We find these points by setting x to 0 for the y-intercept and solving for y, and by setting y to 0 for the x-intercept and solving for x.
Step-by-step explanation:
To determine the x-intercept and y-intercept of the line given by the equation y = 6x + 13, we need to find the points where the line crosses the x-axis and y-axis, respectively.
The y-intercept occurs where the line crosses the y-axis, which is when x=0. Plugging x=0 into the equation, we get y = 6(0) + 13, so y = 13. Thus, the y-intercept is the point (0, 13).
The x-intercept occurs where the line crosses the x-axis, which is when y=0. Solving the equation for x when y=0 gives us 0 = 6x + 13. Subtract 13 from both sides to get -13 = 6x. Then, divide by 6 to get x = -13/6. Therefore, the x-intercept is the point (-13/6, 0).