Question

determine whether the statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement. the graph of the linear function (7x + 6y - 42 = 0) is a line passing through the point ((6,0)) with slope (-\frac{7}{6}). select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the given statement is false. the graph of the linear function (7x + 6y - 42 = 0) is a line passing through the point ((6,0)) with slope (square) (simplify your answer. type an integer or a fraction.)
b. the given statement is false. the graph of the linear function (7x + 6y - 42 = 0) is a line passing through the point (square) with slope (-\frac{7}{6}) (type an ordered pair, using integers or fractions.)
c. the given statement is true.

Explanation:

Step1: Check if (6,0) is on the line

Substitute $x=6, y=0$ into $7x+6y-42=0$:
$7(6)+6(0)-42=42-42=0$. The point satisfies the equation, so it lies on the line.

Step2: Find the slope of the line

Rewrite the equation in slope-intercept form $y=mx+b$:
$6y = -7x + 42$
$y = -\frac{7}{6}x + 7$
The slope $m$ is $-\frac{7}{6}$.

Answer:

C. The given statement is true.