Answer :

An equation of the line in the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

To find the slope of the given line, let's isolate y and find m, according to the steps below.

Step 01: Add 5x to both sides of the equation.

[tex]\begin{gathered} -5x+8y+5x=-18+5x \\ 0+8y=5x-18 \\ 8y=5x-18 \end{gathered}[/tex]

Step 02: Divide both sides by 8.

[tex]\begin{gathered} \frac{8y}{8}=\frac{5x-18}{8} \\ y=\frac{5}{8}x-\frac{18}{8} \\ which\text{ is the same as:} \\ y=\frac{5}{8}x-\frac{9}{4} \end{gathered}[/tex]

Step 03: Compare the equation with the general equation.

[tex]\begin{gathered} y=\frac{5}{8}x-\frac{9}{4} \\ y=mx+b \end{gathered}[/tex]

So, the slope m is 5/8.

Answer: The slope is 5/8.

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