Question

question
find the slope of a line parallel to the line whose equation is 8x + 10y = 60. fully simplify your answer.
answer attempt 1 out of 3
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Explanation:

Step1: Convert to slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We start with the equation \(8x+10y = 60\).
First, we isolate \(y\). Subtract \(8x\) from both sides of the equation: \(10y=-8x + 60\).
Then, divide each term by 10: \(y=\frac{-8x + 60}{10}\).
Simplify the right - hand side: \(y=-\frac{8}{10}x+6\).
Simplify the fraction \(\frac{-8}{10}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \(y =-\frac{4}{5}x + 6\).

Step2: Determine the slope of the parallel line

Parallel lines have the same slope. For the line \(y =-\frac{4}{5}x+6\), the slope \(m\) is \(-\frac{4}{5}\). So, the slope of a line parallel to \(8x + 10y=60\) is also \(-\frac{4}{5}\).

Answer:

\(-\frac{4}{5}\)