In the figure above, what is the equation of the line that passes the y-axis at (0,5) and passes the x-axis at (5,0)?

In the figure above, what is the equation of the line that passes the y-axis at (0,5) and passes the x-axis at (5,0)?

Answer Details

The equation of the line is given by y = x + 5. To understand why, let's consider the two points the line passes through: (0,5) and (5,0). The first point (0,5) means that when x = 0, y = 5. The second point (5,0) means that when y = 0, x = 5. Using these two points, we can write an equation for the line that passes through them. The slope of the line is the difference in y values divided by the difference in x values, or (5 - 0) / (0 - 5) = -1. So the equation of the line is y = -x + b, where b is the y-intercept, or the point where the line crosses the y-axis. To find b, we use the first point (0,5), plug in x = 0, and solve for b: 5 = -0 + b, so b = 5. Putting it all together, the equation of the line is y = -x + 5.