Drawing Straight Line Graphs

• The standard form $y = mx + c$ defines the line's behavior, where $m$ represents the gradient (steepness) and $c$ represents the y-intercept (vertical starting point).

• The gradient is calculated as the ratio of vertical change to horizontal change: $m = \frac{\text{rise}}{\text{run}}$.

• A positive $m$ indicates an upward slope from left to right, while a negative $m$ indicates a downward slope.

Method 1: Table of Values

• Step 1: Select at least three values for $x$ (e.g., $-1, 0, 1$) to ensure the line is straight and accurate.
• Step 2: Substitute each $x$ value into the equation to calculate the corresponding $y$ value.
• Step 3: Plot the resulting $(x, y)$ coordinates on the grid and connect them with a straight edge.

Method 2: Gradient-Intercept Method

• Step 1: Identify the y-intercept $c$ and plot the point $(0, c)$ on the y-axis.
• Step 2: Use the gradient $m$ to find the next point. If $m = \frac{a}{b}$, move $b$ units right and $a$ units up (or down if negative).
• Step 3: Repeat the step to find a third point and draw the line through all points.

• Table of Values is safer for complex equations or fractions, while the Gradient-Intercept method is faster for equations already in $y = mx + c$ form.

• Coordinate Swapping: A common error is plotting $(y, x)$ instead of $(x, y)$. Remember that the first number always dictates horizontal movement.

• Negative Gradient Direction: Students often move 'up' for the rise regardless of the sign. If $m$ is negative, the 'rise' is actually a 'fall' (downward movement).

• Intercept Confusion: Misidentifying the y-intercept as the x-intercept can shift the entire line horizontally, leading to an incorrect graph.