Question

question #6
what is the slope intercept form of the following equation?
y - (-1) = -\frac{2}{3}(x - 9)
linear function test 25

Explanation:

Step1: Simplify the left - hand side

The equation is \(y - (-1)=-\frac{2}{3}(x - 9)\). First, simplify \(y-(-1)\) to \(y + 1\). So the equation becomes \(y+1 = -\frac{2}{3}(x - 9)\).

Step2: Distribute the right - hand side

Using the distributive property \(a(b - c)=ab - ac\), where \(a = -\frac{2}{3}\), \(b=x\) and \(c = 9\), we have:
\(y+1=-\frac{2}{3}x+(-\frac{2}{3})\times(-9)\)
Calculate \((-\frac{2}{3})\times(-9)=\frac{18}{3} = 6\). So the equation is \(y + 1=-\frac{2}{3}x+6\).

Step3: Solve for y

Subtract 1 from both sides of the equation:
\(y=-\frac{2}{3}x+6 - 1\)
Simplify \(6 - 1 = 5\). So \(y=-\frac{2}{3}x+5\).

Answer:

The slope - intercept form of the equation \(y-(-1)=-\frac{2}{3}(x - 9)\) is \(y = -\frac{2}{3}x+5\)