Final answer:
The y-intercept of the line y = 5x - 13 is -13, found by setting x to zero, and the x-intercept is 2.6, found by setting y to zero. The correct answer is option (a).
Step-by-step explanation:
Determining the Intercepts of a Line
To find the y-intercept of the line y = 5x - 13, you need to determine the value of y when x is equal to zero. Substituting x = 0 in the equation, we get y = 5(0) - 13, which simplifies to y = -13. Hence, the y-intercept is -13.
For the x-intercept, you need to determine the value of x when y is equal to zero. Setting y = 0, we have 0 = 5x - 13. Solving for x, you add 13 to both sides to get 13 = 5x, and then divide both sides by 5, resulting in x = 13/5 or x = 2.6. Therefore, the x-intercept is 2.6.
The correct answer is: y-intercept: -13; x-intercept: 2.6, which corresponds to option (a).