Question

Graph the equation. $$x+y=7$$

Short answer

The graph of the equation \(x + y = 7\) is a straight line with a slope of -1 and y-intercept at (0, 7).

Step-by-step solution

Rewrite the equation in standard form y = mx + b

First, you want to get the equation in a form that you can easily create a graph from. To get to the slope-intercept form \(y = mx + b\), where m is the slope and b is the y-intercept, you need to subtract x from both sides of the original equation. This gives you \(y = 7 - x\).

Identify the slope and y-intercept

Once the equation is presented as \(y = 7 - x\), we identify the slope and y-intercept. The number in front of x (in this case, -1) is considered the 'slope' of the line, and the constant term (in this case, 7) is the 'y-intercept'.

Plot the y-intercept

Start by plotting the y-intercept, which in this case is 7. This indicates that the line should pass through the point (0, 7).

Use the slope to identify another point and draw the line

The slope is -1. This means for every 1 unit increase in x, y decreases by 1 unit. Starting from the y-intercept (0, 7), move to the right and down to plot another point at (1,6). You may repeat this to get more points on the line. After plotting the points, connect them to create the line that represents the equation.