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

To find the y-coordinate of a point given its x-coordinate, substitute the x-value into the equation of the line.

When you have the equation of a line, such as y = 2x + 3, you can find the y-coordinate by substituting the given x-coordinate into this equation. For example, if the x-coordinate is 4, you would replace x with 4 in the equation: y = 2(4) + 3. This simplifies to y = 8 + 3, so y = 11. Therefore, the y-coordinate is 11.

If the equation is more complex, like a quadratic equation y = x² - 4x + 6, the process is similar. Suppose the x-coordinate is 2. Substitute 2 into the equation: y = (2)² - 4(2) + 6. This simplifies to y = 4 - 8 + 6, so y = 2. Thus, the y-coordinate is 2.

In some cases, you might have a table of values or a graph instead of an equation. If you have a table, find the row where the x-coordinate matches the given value and read off the corresponding y-coordinate. If you have a graph, locate the given x-coordinate on the x-axis, then move vertically to the point where it intersects the line or curve, and read the y-coordinate from the y-axis.

Understanding how to substitute and simplify expressions is crucial for this process. Practising with different types of equations and using graphs or tables will help you become more confident in finding y-coordinates from given x-coordinates.