Determining Solutions to Equations Using Graphs

This lesson teaches how to determine if a coordinate pair is a solution to an equation by using its graph. It covers graphing equations like X^2 + Y^2 = 25 and X + Y = 4, showing how to plot points and identify the shape of the graph. The lesson also explains how to verify solutions using algebra, demonstrating with examples like (3,2) and (-4,-3).

What shape does the graph of the equation X^2 + y^2 = 25 form?

• A parabola

• A circle

• A line

• An ellipse

Which of the following points is a solution to the equation X + y = 4?

• (2, 2)

• (3, 3)

• (1, 4)

• (0, 5)

Why is the point (3, 2) not a solution to the equation X^2 + y^2 = 25?

• It lies on the curve

• It does not lie on the curve

• It satisfies the equation

• It is outside the graph

How can you verify if a point is a solution to an equation using algebra?

• By plotting the point on a graph

• By substituting the point into the equation

• By drawing a line through the point

• By checking if the point is inside a circle

Which point is confirmed as a solution to the equation X^2 + y^2 = 25?

• (3, 2)

• (-4, -3)

• (5, 5)

• (0, 0)