Final answer:
The line described by the equation -3x + 7y = -21 has a y-intercept of (0, -3), an x-intercept of (7, 0), and a slope of 3/7. The correct multiple-choice answer is (B).
Step-by-step explanation:
To find the x-intercept, y-intercept, and slope of the line described by the equation -3x + 7y = -21, we will need to rearrange the equation into slope-intercept form, which is y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept.
Step 1: Find the y-intercept
To find the y-intercept, we set x = 0 in the equation and solve for y:
-3(0) + 7y = -21
7y = -21
y = -21 / 7
y = -3
Therefore, the y-intercept is (0, -3).
Step 2: Find the x-intercept
To find the x-intercept, we set y = 0 in the equation and solve for x:
-3x + 7(0) = -21
-3x = -21
x = -21 / -3
x = 7
Therefore, the x-intercept is (7, 0).
Step 3: Find the Slope
The slope can be found by isolating y in the equation:
7y = 3x - 21
y = (3/7)x - 3
The coefficient of x, which is 3/7, represents the slope of the line.
Thus, the slope of the line is 3/7.
In conclusion, the x-intercept is (7, 0), the y-intercept is (0, -3), and the slope is 3/7. The correct answer is (B) x-intercept: (7, 0), y-intercept: (0, -3), slope: -3/7.