Problem 12 - Algebra 1: Concepts and Skills

Question

Find the \(x\) -intercept and the \(y\) -intercept of the graph of the equation. Graph the equation. $$ 3 y=-6 x+3 $$

Step-by-Step Solution

Answer

The x-intercept is 0.5 and the y-intercept is 1.

Step 1: Understanding the x-intercept and y-intercept

The x-intercept of the graph of an equation is the point or points where the graph crosses the x-axis. To find the x-intercept, we set y = 0 and solve the equation for x. The y-intercept is the point where the graph crosses the y-axis. To find the y-intercept, we set x = 0 and solve the equation for y.

Step 2: Finding the x-intercept

First, let's set y = 0 in the given equation to find the x-intercept.\n\[3*0 = -6x + 3\]\nThis simplifies to 0 = -6x + 3. Rearrange the equation to solve for x:\n\[-6x = -3\]\nSolving for x gives \(x = 0.5\). So, the x-intercept is 0.5.

Step 3: Finding the y-intercept

Next, let's set x = 0 in the given equation to find the y-intercept.\n\[3y = -6*0 + 3\]\nThis simplifies to 3y = 3. Solving for y gives \(y = 1\). Thus, the y-intercept is 1.

Step 4: Graphing the equation

Now that we have found the x-intercept (0.5, 0) and the y-intercept (0, 1), we can plot these points on the coordinate plane and draw a straight line through these points to represent the equation.