Question

What is the slope of any line parallel to the graph of $\mathbf{6}x+\mathbf{5}y=\mathbf{9}?$

(A) 6

(B) $-\frac{6}{5}$

(C)$\frac{2}{3}$

(D) – 6

Short answer

The slope of line parallel to $6x+5y=9$is $\left(B\right)\frac{-6}{5}.$

Step-by-step solution

– Concept of slope

The slope of a line is defined as the change in $\mathbf{y}-\mathbf{value}$ divided by the change in $\mathbf{x}-\mathbf{value}.$It is also necessary component in a line’s equation and all parallel line have same slope.

– Example to obtain a slope

Let us consider a line $5x+3y=14.$

We know that the line equation is

$y=mx+c$ $....\left(1\right)$

Here, $m$is the slope of the line.

Rearranging the given line equation, we get

$\begin{array}{c}5x+3y=14\\ 3y=14-5x\\ y=\frac{14}{3}-\frac{5}{3}x\\ y=-\frac{5}{3}x+\frac{14}{3}\end{array}$

$....\left(2\right)$

Comparing (1) and (2), we get

$m=\frac{-5}{3}$

Thus, the slope of line is $\frac{-5}{3}.$

– Obtain the solution of the given line

The given graph equation is$6x+5y=9.$

We know that the line equation is

$y=mx+c$

$....\left(1\right)$

Here, $m$is the slope of the line.

Rearranging the given line equation, we get

$\begin{array}{c}6x+5y=9\\ 5y=9-6x\\ y=\frac{9}{5}-\frac{6}{5}x\\ y=-\frac{6}{5}x+\frac{9}{5}\end{array}$

Comparing (1) and (2), we get

$m=\frac{-6}{5}$

The slope of line is $\frac{-6}{5}.$

Since all parallel lines have the same slope, the slope of any line parallel to the graph is$\frac{-6}{5}.$