Question

Graph the equation. Tell whether the equation is a function.

$y=\frac{3}{2}x+1$

Short answer

The equation $y=\frac{3}{2}x+1$ is a function.

Step-by-step solution

Step 1. Given information.

The given equation is $y=\frac{3}{2}x+1$.

Step 2. Calculation.

We can see that our given equation is in slope-intercept form $y=mx+b$, where m represents slope of line and b represents the ­y-intercept.

Upon looking at our given equation, we can see that the slope of our given line is $\frac{3}{2}$ and the ­y-intercept is at point $\left(0,1\right)$.

Upon graphing $y=\frac{3}{2}x+1$, we will get our required graph as shown below:

We can see that no vertical line will intersect the graph of equation $y=\frac{3}{2}x+1$ more than one place that is each x value corresponds to a specific y-value.

Therefore, the equation $y=\frac{3}{2}x+1$ is a function.

Step 3. Conclusion.

The given equation is a function.