Transform the linear equation 4x−8y=24 to slope-intercept form.
To transform the equation from standard form to slope-intercept form, we need to isolate the y variable on one side of the equation.
Starting with the given equation:
4x - 8y = 24
Let's isolate the y term by moving the 4x term to the other side of the equation:
-8y = -4x + 24
Now, divide both sides of the equation by -8 to solve for y:
y = (-4x + 24)/(-8)
Simplifying the right side of the equation:
y = (-1/2)x + 3
The transformed equation in slope-intercept form is:
y = (-1/2)x + 3.
Slope-Intercept Form Quick Check
1 of 51 of 5 Items
Question
Transform the linear equation 4x−8y=24 to slope-intercept form.(1 point)
Responses
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
y=1/2x−3
That is correct! The transformed equation in slope-intercept form is y = (1/2)x - 3. Well done!
Write y−2=3/2(x+2) in slope-intercept form.(1 point)
Responses
y=3/2x+3/2
y=3/2x+6
y=3/2+5x
y=3/2x+5
To write the equation y - 2 = (3/2)(x + 2) in slope-intercept form, we need to simplify and isolate the y variable.
First, let's distribute the (3/2) to both terms inside the parentheses:
y - 2 = (3/2)(x) + (3/2)(2)
y - 2 = (3/2)x + 3
Now, let's move the -2 term to the other side of the equation to isolate the y term:
y = (3/2)x + 3 + 2
Simplifying:
y = (3/2)x + 5
Therefore, the equation in slope-intercept form is y = (3/2)x + 5.
To transform the linear equation 4x - 8y = 24 to slope-intercept form, which is in the form y = mx + b, where "m" represents the slope and "b" represents the y-intercept, follow these steps:
Step 1: Move the term containing "x" to the other side of the equation:
4x - 8y = 24
4x = 8y + 24
Step 2: Divide both sides of the equation by 4 to isolate "x":
(4x)/4 = (8y + 24)/4
x = 2y + 6
Step 3: Rewrite the equation in slope-intercept form by isolating "y":
x = 2y + 6
x - 6 = 2y (subtracted 6 from both sides)
(x - 6)/2 = y (divided both sides by 2)
Thus, the equation 4x - 8y = 24 is transformed to slope-intercept form as y = (1/2)x - 3.
To transform the linear equation 4x - 8y = 24 to slope-intercept form, we need to isolate y on one side of the equation.
Let's begin by rearranging the equation:
4x - 8y = 24
First, we can subtract 4x from both sides of the equation:
-8y = -4x + 24
Next, we divide the entire equation by -8 to solve for y:
y = (-4x + 24) / -8
Simplifying this expression further:
y = -4x/-8 + 24/-8
y = 1/2 * x - 3
Finally, we can write the equation in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept:
y = 1/2 * x - 3
Therefore, the transformed equation in slope-intercept form is y = 1/2 * x - 3.