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We can graph circles and lines on the same coordinate grid and estimate where they intersect. The image shows the circle and the line . The two figures appear to intersect at the points and . To verify whether these truly are intersection points, we can check if substituting them into each equation produces true statements.
Let’s test . First, substitute it into the equation for the line. When we do so, we get . This is a true statement, so this point is on the line.
Next, substitute it into the equation for the circle. This is the same as checking to see if the distance from the point to the center is , or 13 units. We get . Evaluate the left side to get . This is a true statement, so the point is on the circle. It’s on both the circle and the line, so it must be an intersection point for the two figures.