How would you solve y = −x + 1 and y = 2x + 4 graphically?

Question

 On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.

 On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.

 On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

 On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

Answer 1

Hi Nina. I would work on one equation at a time. For y=-x+1, I would first plot the point (0,1) on your graph, because the 1 in the equation is the y-intercept. Then, because there is no number in front of the x, that means the slope of the equation is -1. So from (0,1), it means you can go up 1 space, and to the left 1 space, and plot (-1, 2). Now draw a line between the 2 points, and extend the line above and below the points, and put arrows on both ends.

For y=2x+4, plot (0,4) on the graph. Since there is a 2 in front of the x, it means the slope is 2. That means y increases by 2, while x increases by 1, From (0,4), we can then plot (1,6). Draw a line between the 2 points, and extend the straight line in both directions. Put arrows at both ends. Look for where the 2 graphs cross. That point (-1,2) is the solution, how you solve it graphically.

Answer 2