Final answer:
To graph the line, plot the y-intercept (0,3) and the point (2, 5) on a coordinate plane, then draw a straight line through these points. The line's slope is calculated as 1, making the equation of the line y = x + 3.
Step-by-step explanation:
To graph a line with a y-intercept of 3 and containing the point (2, 5), we first plot the y-intercept (0,3) on the coordinate plane. We then plot the second point given in the question, which is (2, 5). Once these two points are plotted, draw a straight line through them, and you have graphed the line.
If we need to calculate the slope of this line, we can use the two points. The slope formula is (y2 - y1) / (x2 - x1), which gives us (5 - 3) / (2 - 0) = 2 / 2 = 1. Therefore, the slope of the line is 1, and the line would rise 1 unit for every 1 unit it goes to the right.
The equation of the line can be written in slope-intercept form (y = mx + b) using the slope we just calculated and the y-intercept: y = 1x + 3.