y-1/x+3=-3/4 solving for y. Please show steps so that I can get a better understanding of this.
y-1/x+3=-3/4
y-1/x+ 1/x + 3-3 = -3/4 + 1/x -3
y - 0 + 0 = -3/4 - 3 + 1/x
y = (-3 - 12)/4 + 1/x
y = -15/4 + 1/x
Assuming the usual carelessness with parentheses, I see it as follows:
(y-1)/(x+3) = -3/4
y-1 = -3/4 (x+3)
y = -3/4 (x+3) + 1
y = -3/4 x - 5/4
y = -(3x+5)/4
To solve the equation y-1/x+3=-3/4 for y, we need to isolate the variable y on one side of the equation. Here are the steps to solve it:
Step 1: Multiply both sides of the equation by x+3 to clear the denominator.
(x+3) * (y-1/x+3) = (x+3) * (-3/4)
(y-1) = (-3/4) * (x+3)
Step 2: Distribute (-3/4) to (x+3) on the right side of the equation.
(y-1) = (-3/4) * x + (-3/4) * 3
Step 3: Simplify the right side of the equation.
(y-1) = (-3/4) * x - 9/4
Step 4: Move -1 to the right side of the equation by adding it to both sides.
y = (-3/4) * x - 9/4 + 1
Step 5: Simplify the equation further.
y = (-3/4) * x - 9/4 + 4/4
Step 6: Combine like terms on the right side.
y = (-3/4) * x - 5/4
The equation is now in the form y = mx + b, which represents a linear equation. The coefficient (-3/4) is the slope, and (-5/4) is the y-intercept.