Question

the equation of a line is given below.
-7x + 6y = -21
(a) find the x-intercept and the y-intercept.
x-intercept:
y-intercept:
(b) use the intercepts to graph the line.

Explanation:

Step1: Find x-intercept (set y=0)

Set \( y = 0 \) in \( -7x + 6y = -21 \):
\( -7x + 6(0) = -21 \)
\( -7x = -21 \)
Divide by -7: \( x = \frac{-21}{-7} = 3 \).

Step2: Find y-intercept (set x=0)

Set \( x = 0 \) in \( -7x + 6y = -21 \):
\( -7(0) + 6y = -21 \)
\( 6y = -21 \)
Divide by 6: \( y = \frac{-21}{6} = -\frac{7}{2} = -3.5 \).

Answer:

x-intercept: \( 3 \)
y-intercept: \( -\frac{7}{2} \) (or \( -3.5 \))

(For part (b), plot the points \( (3, 0) \) (x-intercept) and \( (0, -\frac{7}{2}) \) (y-intercept) on the graph and draw a line through them.)