Final answer:
To graph the equation 2x+y=7, rearrange it to the form y=mx+b, plot the y-intercept and use the slope to find additional points. The point (3,4) does lie on the graph.
Step-by-step explanation:
To graph the equation 2x+y=7, we can rearrange it to the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope m is -2 and the y-intercept b is 7. So, the equation becomes y=-2x+7.
To graph the equation, we can plot the y-intercept at (0,7) and use the slope to find additional points. The slope -2 means that for every 1 unit increase in x, y decreases by 2 units. So, from the y-intercept (0,7), we can go 1 unit to the right and 2 units down to get the point (1,5). We can repeat this process to find more points.
Now, let's check if the point (3,4) lies on the graph. Substitute x=3 and y=4 into the equation y=-2x+7: 4=-2(3)+7. Simplifying this equation, we get 4=-6+7, which is true. Therefore, the point (3,4) does lie on the graph.