How do you graph 2x + y = 5 by plotting points?

To graph the equation 2x + y = 5 by plotting points, follow these steps:

Rewrite the equation in slope-intercept form (y = mx + b): The given equation is 2x + y = 5. To solve for y, subtract 2x from both sides: y = -2x + 5.

This equation is now in the form y = mx + b, where m is the slope and b is the y-intercept.

Identify the y-intercept: From the equation y = -2x + 5, we can see that the y-intercept is 5. This means the graph will cross the y-axis at the point (0, 5).

Find a second point using the slope: The slope is -2, which means that for every 1 unit you move to the right (positive x-direction), you move 2 units down (negative y-direction).

Starting at the point (0, 5), move 1 unit to the right (x = 1), and then move 2 units down (y = 5 - 2 = 3). This gives the second point (1, 3).

Plot the points:

Plot the point (0, 5) on the graph (this is the y-intercept).
Plot the point (1, 3) using the slope.
Draw the line: Once you have at least two points, draw a straight line through them. This line represents the equation 2x + y = 5.

So, the graph of the equation 2x + y = 5 is a straight line passing through the points (0, 5) and (1, 3).