find the slope and y-intercept of the graph of the equation. explain each step and how you got it.
12x + 4y= 24
-first you move the 12x to the other side of the equation to isolate the 4y
-Divide the whole equation by 4 to give a single y
-this gives you y=-3x+6
-the slope is -3 because your "m" term is the slops in a standard equation(which you have)
-the y-intercept is found by setting y to 0. you would solve: 0=-3x+6 which gives you 2. (isolate the -3x; divide by -3 to give a single unit)
That's it!
To find the slope and y-intercept of the graph of the equation 12x + 4y = 24, follow these steps:
Step 1: Move the 12x term to the other side of the equation to isolate the 4y term.
12x + 4y = 24
Subtract 12x from both sides:
4y = -12x + 24
Step 2: Divide the whole equation by 4 to give a single y term.
Divide both sides of the equation by 4:
y = (-12/4)x + 24/4
Simplify the equation:
y = -3x + 6
Step 3: Identify the slope.
In the equation y = -3x + 6, the coefficient of x (-3) is the slope. Therefore, the slope is -3.
Step 4: Find the y-intercept.
The y-intercept is the value of y when x is equal to 0. To find it, we substitute x = 0 into the equation y = -3x + 6:
y = -3(0) + 6
y = 6
Therefore, the y-intercept is 6.
In summary, the equation 12x + 4y = 24 can be rewritten as y = -3x + 6. The slope is -3, and the y-intercept is 6.