Question

Determine the slope of the line represented by the equation -5x+8y= -18

Answer 1

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.

`\begin{gathered} -5x+8y+5x=-18+5x \\ 0+8y=5x-18 \\ 8y=5x-18 \end{gathered}`

Step 02: Divide both sides by 8.

`\begin{gathered} (8y)/(8)=(5x-18)/(8) \\ y=(5)/(8)x-(18)/(8) \\ which\text{ is the same as:} \\ y=(5)/(8)x-(9)/(4) \end{gathered}`

Step 03: Compare the equation with the general equation.

`\begin{gathered} y=(5)/(8)x-(9)/(4) \\ y=mx+b \end{gathered}`

So, the slope m is 5/8.

Answer: The slope is 5/8.