Transform the linear equation 4x−8y=24 to slope-intercept form.(1 point)
Responses
y=12x−3
y equals Start Fraction 1 over 2 End Fraction x minus 3
4x−8y−24=0
4 x minus 8 y minus 24 equals 0
−8y=−4x+24
negative 8 y equals negative 4 x plus 24
4x−8y=24
4 x minus 8 y equals 24
To transform the linear equation 4x-8y=24 to slope-intercept form, we want to isolate y on one side of the equation.
4x - 8y = 24
We can start by subtracting 4x from both sides:
-8y = -4x + 24
Next, we divide both sides by -8 to solve for y:
y = (-4x + 24)/-8
Finally, we simplify the right side of the equation:
y = -1/2x + 3
To transform the linear equation 4x - 8y = 24 to slope-intercept form, follow these steps:
1. Move the term containing the variable "x" to the other side of the equation:
4x - 8y + 8y = 24 + 8y
Simplifying, we get:
4x = 8y + 24
2. Divide both sides of the equation by 4 to isolate the "x" term:
(4x)/4 = (8y + 24)/4
Simplifying further, we get:
x = 2y + 6
3. Now, rewrite the equation in slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept:
x = 2y + 6
Reorder the equation to match the slope-intercept form:
2y = x - 6
Divide both sides of the equation by 2:
(2y)/2 = (x - 6)/2
Simplifying, we get:
y = (1/2)x - 3
Therefore, the given linear equation 4x - 8y = 24 can be written in slope-intercept form as y = (1/2)x - 3.
To transform the linear equation 4x - 8y = 24 to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, follow these steps:
Step 1: Move the constant term to the other side of the equation.
4x - 8y = 24
4x - 24 = 8y
Step 2: Divide the entire equation by the coefficient of y to isolate y.
(4x - 24)/8 = y
(1/2)x - 3 = y
Therefore, the equation is y = (1/2)x - 3, which is in slope-intercept form. The slope (m) is 1/2, and the y-intercept (b) is -3.