Free graphing resources · Original practice
Graph four lines from standard-form equations by finding x- and y-intercepts. Keep zero and negative intercepts as valid coordinates.
Graph four lines from standard-form equations by finding x- and y-intercepts. Keep zero and negative intercepts as valid coordinates.
Choose Letter or A4, then download a student sheet first. Keep the separate reference or answer file closed until you have attempted the case. Every worksheet, SVG and answer is free without signup.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Complete free PDF pack.
| Case | Focus |
|---|---|
| ST01 | Positive intercepts |
| ST02 | A falling line |
| ST03 | A line through the origin |
| ST04 | Mixed signs |
All examples use original fictional data and coordinate units. They are practice material, not measured classroom results, published questions or evidence about real people.
ST01: Positive intercepts
| Check | Worked result |
|---|---|
| 1 | x-intercept 6; y-intercept 4. |
| 2 | Equation 2x + (3)y = 12. |
| 3 | Use two intercepts to draw the line. |
The first case shows the checking pattern. Individual answer files contain the completed graph and result for every case.
Begin by identifying the specific linear equation provided in the resource, such as the example with coefficients two and three equaling twelve. To locate the x-intercept, substitute zero for the variable y in the equation. Solve the resulting arithmetic expression to determine the numerical value of x. This calculated value represents the horizontal coordinate where the line crosses the axis. Record this number precisely as it will serve as one of the two anchor points needed for drawing. Ensure you use the exact equation supplied in the listed file rather than estimating from any visual representation of the line.
Next, determine the vertical crossing point by setting the variable x to zero within the same linear equation. For instance, in the case where coefficients are three and negative two equaling six, substitute zero for x and solve for y. The resulting value is the y-intercept coordinate. This step is critical because it provides the second anchor point required to define the line's position on the grid. Remember that a zero intercept is a valid result, particularly in cases where the line passes through the origin. Use the supplied values to calculate this coordinate accurately without relying on visual estimation.
With both intercept coordinates calculated, locate these two points on the provided listed coordinate grid. Plot the x-intercept on the horizontal axis and the y-intercept on the vertical axis. Use a straightedge to connect these two distinct points, extending the line across the grid. The accuracy of the drawn line depends entirely on the precision of the calculated intercepts derived from the exact equation. Do not adjust the line to match a perceived appearance; instead, trust the mathematical coordinates determined by the coefficients. This method ensures the graphical representation aligns perfectly with the algebraic definition provided in the original fictional practice material.
| Watch for | Check instead |
|---|---|
| Estimating the line's position by looking at the printed graph rather than calculating the intercepts from the equation coefficients. | Always calculate the x and y intercepts by substituting zero for the opposite variable in the exact equation provided, then plot those specific coordinates. |
| Assuming a line must cross both axes at non-zero values and discarding a result where the intercept is zero. | Recognize that a zero intercept is valid, especially when the constant term is zero, indicating the line passes through the origin as seen in specific cases. |
| Ignoring negative coefficients in the equation, leading to incorrect signs for the calculated intercept coordinates. | Carefully apply the negative signs from the supplied coefficients A and B when solving for the intercepts to ensure the plotted points are in the correct quadrants. |
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Set y to zero and solve for x. For a y-intercept, set x to zero and solve for y.
Yes. A line through the origin can have both intercepts at (0,0).
Keep the sign when solving. A negative intercept is a valid coordinate result.
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