Question

Determine the intercepts of the line \(6x - 3y = -7\).

A. x-intercept: \((-7/6, 0)\), y-intercept: \((0, 7/3)\)
B. x-intercept: \((-7/6, 0)\), y-intercept: \((0, -7/3)\)
C. x-intercept: \((0, 7/3)\), y-intercept: \((-7/6, 0)\)
D. x-intercept: \((0, -7/3)\), y-intercept: \((-7/6, 0)\)

Answer 1

The correct intercepts of the given line 6x - 3y = -7 are the x-intercept at (-7/6, 0) and the y-intercept at (0, 7/3), which matches option A.

Step-by-step explanation:

To determine the x-intercept and y-intercept of the line, we need to find where the line crosses the x-axis and y-axis respectively. For the x-intercept, the y-value is zero, and for the y-intercept, the x-value is zero.

Starting with the x-intercept, set y to 0 in the equation:
6x - 3×0 = -7

1. 6x = -7
2. x = -7/6

The x-intercept is (

-7/6

, 0).

Next, for the y-intercept, set x to 0 in the equation:
6×0 - 3y = -7

1. -3y = -7
2. y = 7/3

The y-intercept is (0,

7/3

).

Therefore, the correct intercepts of the line are the x-intercept: (-7/6, 0) and the y-intercept: (0, 7/3). This corresponds to option A.