4

To complete the table and find the x- and y-intercepts for the equation \( y = -2x + 3 \), follow these steps:

Table of Values

Choose values for \( x \) and calculate the corresponding \( y \) values.

1. Let \( x = 0 \): \[ y = -2(0) + 3 = 3 \] So, \( (0, 3) \).

2. Let \( x = 1 \): \[ y = -2(1) + 3 = 1 \] So, \( (1, 1) \).

3. Let \( x = 2 \): \[ y = -2(2) + 3 = -1 \] So, \( (2, -1) \).

Now the table can be filled in as:

\[ \begin{array}{c|c} x & y \\ \hline 0 & 3 \\ 1 & 1 \\ 2 & -1 \\ \end{array} \]

X-Intercept

To find the x-intercept, set \( y = 0 \) and solve for \( x \).

\[ 0 = -2x + 3 \\ 2x = 3 \\ x = \frac{3}{2} \]

So, the x-intercept is \( \left(\frac{3}{2}, 0\right) \).

Y-Intercept

To find the y-intercept, set \( x = 0 \) which we've already calculated:

\[ y = 3 \]

So, the y-intercept is \( (0, 3) \).

These points are useful for graphing the linear equation.