Question

Use a table of values to graph the equation. $$-2 x+2 y=5$$

Short answer

The graph of the equation \(-2x + 2y = 5\) is a straight line that passes through the points \((-1, 1.5), (0, 2.5), (1, 3.5), (2, 4.5)\)

Step-by-step solution

Rewrite The Equation in y=mx+b Form

First, transform the equation \( -2x + 2y = 5 \) into slope-intercept form, \(y = mx + b\), where m is the slope and b is the y-intercept. The given equation can be rewritten as \(y = x + 2.5\)

Constructing The Table

Choose a few reasonable values for x and substitute them in the equation \(y = x + 2.5\) to obtain the corresponding values for y. For instance, we can take x = -1, 0, 1 and 2.

Compute Corresponding Y Values

Substitute the chosen x values in the equation to get y values. For instance, if x = -1, \(y = -1 + 2.5 = 1.5\). If x = 0, \(y = 0 + 2.5 = 2.5\). If x = 1, \(y = 1 + 2.5 = 3.5\). If x = 2, \(y = 2 + 2.5 = 4.5\).

Plotting The Graph

Plot the pairs of x and y values on the plane as points. The pairs are \((-1, 1.5), (0, 2.5), (1, 3.5), (2, 4.5)\). After plotting these points, draw a line that passes through them.