Question

What is the slope of a line parallel to the line whose equation is 12x – 15y = 315.Fully simplify your answer.

Answer 1

4/5

Step-by-step explanation:

Definition: Two lines are parallel if they have the same slope.

Given the line:

`12x-15y=315`

Determine the slope of the given line by expressing it in the slope-intercept form (y=mx+b), where m is the slope:

`\begin{gathered} 12x-15y=315 \\ \text{ Add 15y to both sides of the equation} \\ 12x-15y+15y=315+15y \\ 12x=315+15y \\ \text{ Subtract 315 from both sides:} \\ 12x-315=315-315+15y \\ 12x-315=15y \\ \text{ Divide all through by 15} \\ (15y)/(15)=(12)/(15)x-(315)/(15) \\ y=(4)/(5)x-21 \end{gathered}`

• The slope of the line, m = 4/5.

Since the lines are parallel, they have the same slope.

Hence, the slope of a line parallel to the line whose equation is 12x – 15y = 315 is 4/5.