Solve for $y$.
$
9 x-3 y=-15 \
y=[?] x+\square
$
Answer (1)
Subtract 9 x from both sides of the equation: − 3 y = − 9 x − 15 .
Divide both sides by − 3 to solve for y : y = − 3 − 9 x − 15 .
Simplify the equation: y = 3 x + 5 .
The equation is now in the form y = [ ?] x + □ , so the solution is y = 3 x + 5 .
Explanation
Understanding the Problem We are given the equation 9 x − 3 y = − 15 and we want to solve for y and express the equation in the form y = [ ?] x + □ . This form is known as the slope-intercept form of a linear equation, where the coefficient of x represents the slope and the constant term represents the y-intercept.
Isolating the y-term First, we want to isolate the term with y on one side of the equation. To do this, we subtract 9 x from both sides of the equation: 9 x − 3 y − 9 x = − 15 − 9 x − 3 y = − 9 x − 15
Solving for y Next, we want to solve for y by dividing both sides of the equation by − 3 :
− 3 − 3 y = − 3 − 9 x − 15 y = − 3 − 9 x + − 3 − 15 y = 3 x + 5
Finding the Slope and Intercept Now we have the equation in the form y = 3 x + 5 , which matches the desired form y = [ ?] x + □ . Therefore, the coefficient of x is 3 and the constant term is 5 .
Examples
Understanding how to convert a linear equation to slope-intercept form is useful in many real-world scenarios. For example, if you are tracking the cost of a service that charges a fixed fee plus an hourly rate, you can use the slope-intercept form to model the total cost. If a plumber charges a $50 service fee plus $75 per hour, the equation would be y = 75 x + 50 , where y is the total cost and x is the number of hours. This allows you to easily determine the total cost for any number of hours of work.
