A slope intercept form from graph worksheet helps you turn a line on a coordinate plane into an equation in y = mx + b form. The two key jobs are finding the y-intercept and identifying the slope. Once you know those values, writing the equation becomes straightforward and you can check whether it matches the line you see on the graph.
Find the Y-Intercept
Start with the y-intercept, which is the point where the line crosses the y-axis. On a graph, this is where x equals 0, so the value of y at that point becomes b in y = mx + b. If the line crosses at (0, 3), then b is 3. If it crosses below the origin, b is negative. This step is usually the easiest part of the worksheet because it comes directly from the graph.
Next, find the slope by using two clear points on the line. Choose points where the line passes through grid intersections, then count rise over run. For example, if moving from one point to another goes up 2 and right 4, the slope is 2/4, which simplifies to 1/2. If the line goes down as you move right, the slope is negative. Keep the rise and run in the same order each time so the sign stays correct.
Write the Equation
After you know m and b, plug them into y = mx + b. If the slope is 1/2 and the y-intercept is 3, the equation is y = 1/2x + 3. If the slope is negative 2 and the y-intercept is -1, the equation becomes y = -2x – 1. This is the final form the worksheet is asking for, so keep the variable y on the left and the slope and intercept on the right.
Finish by checking your equation against the graph. See whether the y-intercept matches the point where the line crosses the y-axis, then test the slope by starting at that point and using rise over run. If the line and the equation lead to the same next point, your answer is likely correct. This quick check helps you catch sign mistakes and makes the worksheet much easier to complete with confidence.
