Question

Determine the intercepts of the line:

y = 5x - 13
y-intercept: ____ (blank)
x-intercept: ____ (blank)
a) y-intercept: -13; x-intercept: 2.6
b) y-intercept: 5; x-intercept: 13
c) y-intercept: -13; x-intercept: -2.6
d) y-intercept: 13; x-intercept: -2.6

Answer 1

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).