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Math  /  Algebra

QuestionPut the following equation of a line into slope-intercept form, simplifying all fractions. 20x−8y=4020 x-8 y=40

Studdy Solution

STEP 1

1. The equation given is a linear equation.
2. We need to convert the equation into slope-intercept form, which is y=mx+b y = mx + b , where m m is the slope and b b is the y-intercept.
3. Simplifying fractions involves reducing them to their simplest form.

STEP 2

1. Isolate the y y -term on one side of the equation.
2. Solve for y y to express the equation in slope-intercept form.
3. Simplify any fractions that appear in the equation.

STEP 3

Start with the given equation:
20x−8y=40 20x - 8y = 40
Subtract 20x 20x from both sides to isolate the y y -term:
−8y=−20x+40 -8y = -20x + 40

STEP 4

Divide every term by −8-8 to solve for y y :
y=−20x−8+40−8 y = \frac{-20x}{-8} + \frac{40}{-8}

STEP 5

Simplify the fractions:
y=208x−408 y = \frac{20}{8}x - \frac{40}{8}
Reduce the fractions:
y=52x−5 y = \frac{5}{2}x - 5
Now, the equation is in slope-intercept form y=mx+b y = mx + b , where m=52 m = \frac{5}{2} and b=−5 b = -5 .

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