Rewrite each of the following equations in y=mx+b form. Show each step!
y-4=-3(x-3)
To rewrite the equation y-4=-3(x-3) in y=mx+b form, we will start by distributing the -3 to both terms inside the parentheses:
y - 4 = -3x + 9
Next, we will isolate the variable y by adding 4 to both sides of the equation:
y = -3x + 9 + 4
Simplifying:
y = -3x + 13
Thus, the equation is now in y=mx+b form.
Step 1: Distribute the -3 on the right side of the equation.
y-4 = -3x + 9
Step 2: Bring the constant term (-4) to the other side by adding 4 to both sides of the equation.
y = -3x + 9 + 4
Step 3: Simplify the right side of the equation.
y = -3x + 13
Step 4: The equation is now in y=mx+b form, where m is the slope (-3) and b is the y-intercept (13).
To rewrite the equation in y=mx+b form, we need to isolate the y variable on one side.
Step 1: Distribute the -3 to both terms inside the parentheses.
y - 4 = -3x + 9
Step 2: Move -4 to the right side of the equation by adding 4 to both sides.
y = -3x + 9 + 4
Step 3: Combine like terms.
y = -3x + 13
Therefore, the given equation, y-4=-3(x-3), can be rewritten in y=mx+b form as y = -3x + 13.