transform the linear equation 4x - 8y = 24 to slope-intercept form
To transform the equation 4x - 8y = 24 to slope-intercept form, which is in the form y = mx + b, we need to solve for y.
First, isolate y by subtracting 4x from both sides:
-8y = -4x + 24
Next, divide every term by -8 to solve for y:
y = (-4x + 24)/-8
Simplifying the equation further, we have:
y = -1/2x + 3
Therefore, the equation 4x - 8y = 24, when transformed to slope-intercept form, becomes y = -1/2x + 3.
To transform the given linear equation 4x - 8y = 24 to slope-intercept form, which is in the form of y = mx + b, where:
- y represents the value of the dependent variable,
- x represents the value of the independent variable,
- m represents the slope of the line, and
- b represents the y-intercept,
we can follow these steps:
Step 1: Begin with the original equation: 4x - 8y = 24.
Step 2: Move the constant term to the other side of the equation by subtracting 24 from both sides:
4x - 8y - 24 = 0.
Step 3: Divide each term by -8 to isolate y and write the equation in slope-intercept form:
-8y = -4x + 24.
Dividing each term by -8:
y = (1/2)x - 3.
Therefore, the linear equation 4x - 8y = 24, when transformed to slope-intercept form, becomes y = (1/2)x - 3.
To transform the linear equation 4x - 8y = 24 into slope-intercept form, which is of the form y = mx + b, where m represents the slope and b represents the y-intercept, we need to isolate y on one side of the equation.
Let's start by subtracting 4x from both sides of the equation:
4x - 4x - 8y = 24 - 4x
This simplifies to:
-8y = -4x + 24
Next, we divide both sides of the equation by -8 to solve for y:
-8y / -8 = (-4x + 24) / -8
This simplifies to:
y = (4/8)x - 3
Now we can further simplify by reducing the fraction 4/8:
y = (1/2)x - 3
Therefore, the linear equation 4x - 8y = 24 can be transformed into slope-intercept form as y = (1/2)x - 3, with a slope of 1/2 and a y-intercept of -3.