Math  /  Algebra

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Find the slope of a line parallel to the line whose equation is 8x+10y=608 x+10 y=60. Fully simplify your answer. Answer Attempt 2 out of 2

Studdy Solution

STEP 1

What is this asking? We need to find the slope of a line that's parallel to another line, and that other line's equation is 8x+10y=608x + 10y = 60. Watch out! Parallel lines have the *same* slope, so we just need the slope of the given line.
Don't mix it up with perpendicular lines!

STEP 2

1. Rewrite the equation
2. Identify the slope

STEP 3

We want to rewrite the equation 8x+10y=608x + 10y = 60 in slope-intercept form (y=mx+by = mx + b), where mm is the **slope** and bb is the **y-intercept**.
To do this, we need to isolate yy.
Let's **subtract** 8x8x from both sides of the equation:
8x+10y8x=608x8x + 10y - 8x = 60 - 8x10y=8x+6010y = -8x + 60

STEP 4

Now, we **divide** both sides of the equation by 1010 to completely isolate yy:
10y10=8x+6010\frac{10y}{10} = \frac{-8x + 60}{10}y=8x10+6010y = \frac{-8x}{10} + \frac{60}{10}y=810x+6y = -\frac{8}{10}x + 6

STEP 5

Let's **simplify** that fraction by dividing both the numerator and the denominator by their greatest common divisor, which is **2**:
y=8÷210÷2x+6y = -\frac{8 \div 2}{10 \div 2}x + 6y=45x+6y = -\frac{4}{5}x + 6

STEP 6

Remember, slope-intercept form is y=mx+by = mx + b, where mm is the **slope**.

STEP 7

Our equation is now y=45x+6y = -\frac{4}{5}x + 6.
Matching this to the slope-intercept form, we see that our **slope** mm is 45-\frac{4}{5}.
Awesome!

STEP 8

The slope of the given line is 45-\frac{4}{5}.
Since parallel lines have the same slope, the slope of a line parallel to the given line is also 45-\frac{4}{5}.

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