Final answer:
To graph a line with a y-intercept of 5 and containing the point (2, 7), we can use the slope-intercept form of a linear equation, which is y = mx + b. The slope is 1, and the equation is y = 1x + 5. The graph can be plotted by using the y-intercept and the slope to find two points on the line.
Step-by-step explanation:
To graph a line with a y-intercept of 5 and containing the point (2, 7), we can use the slope-intercept form of a linear equation, which is y = mx + b. Here, 'm' represents the slope, and 'b' represents the y-intercept. Since we are given the y-intercept is 5, we have b = 5.
To find the slope, we can use the given point (2, 7) and the y-intercept (0, 5). The slope is determined by the change in y divided by the change in x. So, slope (m) = (7 - 5)/(2 - 0) = 2/2 = 1.
Now we have the equation y = 1x + 5. To graph this line, we can plot the y-intercept at (0, 5) and use the slope to find another point on the line. Since the slope is 1, we can move 1 unit up vertically and 1 unit to the right horizontally from the y-intercept to find another point on the line. This gives us the point (1, 6).