Put the following equation of a line into slope-intercept form, simplifying all fractions.
6x+4y=12
that is not slope-intercept form, which should be
y = -3/2 x + 3
Apologies for the mistake. You are correct. The slope-intercept form of the equation 6x + 4y = 12 is indeed:
y = -3/2x + 3
To put the equation of a line into slope-intercept form, which is in the form y = mx + b, where m represents the slope and b represents the y-intercept, we need to solve for y.
Let's start with the given equation:
6x + 4y = 12
To simplify fractions, we can multiply both sides of the equation by the reciprocal of the coefficient of y, which is 4/1, or simply 4:
(4/1)(6x + 4y) = (4/1)(12)
24x + 16y = 48
Now, we want to isolate y on one side of the equation. Rewrite the equation to isolate the term with y on the left side:
16y = -24x + 48
To simplify further, divide both sides of the equation by 16:
(16y)/16 = (-24x + 48)/16
y = (-24/16)x + 48/16
Simplifying the right side gives:
y = (-3/2)x + 3
So, the original equation 6x + 4y = 12, when simplified and rewritten in slope-intercept form, is y = (-3/2)x + 3.
To put the equation 6x + 4y = 12 into slope-intercept form, we need to isolate y on one side of the equation.
First, let's move the 6x term to the right side:
4y = 12 - 6x
Next, we divide both sides of the equation by 4 to simplify the fractions:
y = (12 - 6x)/4
Finally, let's simplify further:
y = (6 - 3x)/2
This is the equation in slope-intercept form, where the slope is -3/2 and the y-intercept is 6/2 = 3.