Put the following equation of a line into slope-intercept form, simplifying all fractions.
20x−8y=40
To put the equation into slope-intercept form, we need to isolate y on one side of the equation. Let's simplify the equation by dividing every term by 8:
20x - 8y = 40
(20x - 8y)/8 = 40/8
2.5x - y = 5
Finally, let's rearrange the equation to solve for y:
-y = -2.5x + 5
y = 2.5x - 5
To put the equation of a line into slope-intercept form, we need to isolate the variable y on one side of the equation. Let's start solving step-by-step:
1. Begin with the given equation: 20x - 8y = 40.
2. To simplify the equation and get rid of the coefficient of x, divide both sides of the equation by 20:
(20x - 8y)/20 = 40/20.
3. Simplifying, we have: x - (8/20)y = 2.
4. Next, simplify the fraction (8/20). Both the numerator and denominator are divisible by 4:
x - (2/5)y = 2.
5. Finally, rearrange the equation to isolate y on one side, giving it the slope-intercept form y = mx + b:
-(2/5)y = -x + 2.
6. To simplify further, divide both sides of the equation by -(2/5):
y = (-x + 2)/-(2/5).
7. Simplifying the fraction -(2/5), we get:
y = (-x + 2) * (-5/2).
8. Expanding the expression on the right side:
y = (-5/2)(-x) + (-5/2)(2).
9. Simplifying, we have:
y = (5/2)x - 5.
Therefore, the equation 20x - 8y = 40 can be written in slope-intercept form as y = (5/2)x - 5.
To put the given equation of a line into slope-intercept form, we need to isolate y on one side and simplify any fractions. The slope-intercept form of a linear equation is given by the equation y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Let's begin by rearranging the equation 20x - 8y = 40:
Start by subtracting 20x from both sides of the equation:
-8y = -20x + 40
Next, divide every term in the equation by -8 to isolate y:
y = (-20x + 40) / -8
Now, let's simplify any fractions:
y = -20x / -8 + 40 / -8
Simplifying the fractions:
y = 5/2 * x - 5
Therefore, the given equation 20x - 8y = 40, when simplified and written in slope-intercept form, becomes y = 5/2 * x - 5.