How do you find the x-coordinate of a point given its y-coordinate?

To find the x-coordinate given the y-coordinate, substitute the y-value into the equation and solve for x.

When you have a point on a graph and you know its y-coordinate, you can find the corresponding x-coordinate by using the equation of the line or curve that the point lies on. For example, if the equation of the line is \( y = 2x + 3 \) and you know that the y-coordinate is 7, you would substitute 7 for y in the equation to get \( 7 = 2x + 3 \).

Next, you need to solve this equation for x. Start by isolating the term with x on one side of the equation. Subtract 3 from both sides to get \( 4 = 2x \). Then, divide both sides by 2 to solve for x, giving you \( x = 2 \). So, the x-coordinate corresponding to the y-coordinate of 7 is 2.

This method works for any type of equation, whether it’s linear, quadratic, or another form. For a quadratic equation like \( y = x^2 + 2x + 1 \), if you know the y-coordinate, you substitute it into the equation and solve for x, which might involve factoring or using the quadratic formula. For instance, if \( y = 5 \), you would set up the equation \( 5 = x^2 + 2x + 1 \) and solve for x.

Remember, some equations might have more than one x-coordinate for a given y-coordinate, especially in the case of parabolas or circles. Always check for all possible solutions.