How would you write an equation based on a graph?

How would you write an equation based on a graph?

• A. Find 2 coordinates to get slope, identify the y-intercept, then plug in a possible x to get y.
• B. Plot a single point and draw a line through it.
• C. Solve for x when y equals 0.
• D. Use a random slope and intercept without considering the graph.

Answer: (A)

Interpreting a graph to write a linear equation relies on finding the slope and the y-intercept from the graph. Look for two points on the line, preferably where it passes through grid points, and compute the slope m = Δy/Δx. The y-intercept is where the line crosses the y-axis, giving b when x = 0. With m and b you can form the equation y = mx + b, and you can check by plugging in another x-value to see that the y matches the line on the graph. The other approaches don’t provide enough information: a single point doesn’t fix the slope, the x-intercept alone isn’t enough for the full equation, and choosing a slope and intercept without regard to the graph ignores the data shown.

Interpreting a graph to write a linear equation relies on finding the slope and the y-intercept from the graph. Look for two points on the line, preferably where it passes through grid points, and compute the slope m = Δy/Δx. The y-intercept is where the line crosses the y-axis, giving b when x = 0. With m and b you can form the equation y = mx + b, and you can check by plugging in another x-value to see that the y matches the line on the graph. The other approaches don’t provide enough information: a single point doesn’t fix the slope, the x-intercept alone isn’t enough for the full equation, and choosing a slope and intercept without regard to the graph ignores the data shown.