Put the following equation of a line into slope-intercept form, simplifying all fractions.
3x+6y=36
To put the equation 3x + 6y = 36 into slope-intercept form, we need to solve for y.
Starting with the given equation:
3x + 6y = 36
We can begin by isolating y on one side. To do so, we can subtract 3x from both sides:
6y = -3x + 36
Next, we can further isolate y by dividing both sides by 6:
(6y)/6 = (-3x + 36)/6
This simplifies to:
y = (-3/6)x + 6
Now, to simplify the fraction (-3/6), we can divide both the numerator and denominator by their greatest common divisor, which is 3:
y = (-1/2)x + 6
Thus, the equation 3x + 6y = 36 is simplified to y = (-1/2)x + 6 in slope-intercept form.
To put the equation 3x + 6y = 36 into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, follow these steps:
Step 1: Move the term with "x" to the right-hand side of the equation.
3x + 6y = 36 → 6y = -3x + 36
Step 2: Divide each term by the coefficient of y to isolate it.
6y = -3x + 36 → y = (-3/6)x + 36/6
Step 3: Simplify the fractions.
y = (-1/2)x + 6
The equation 3x + 6y = 36, when simplified and rearranged, becomes y = (-1/2)x + 6 in slope-intercept form.
To put the equation of a line into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we need to isolate y on one side of the equation.
Given equation: 3x + 6y = 36
Step 1: Move the term with x to the other side of the equation.
Subtract 3x from both sides:
6y = -3x + 36
Step 2: Divide the entire equation by the coefficient of y to simplify the fraction.
Divide both sides of the equation by 6:
(6y)/6 = (-3x + 36)/6
Simplifying further:
y = -1/2x + 6
The simplified equation in slope-intercept form is y = -1/2x + 6. The slope is -1/2, and the y-intercept is 6.