Plot and interpret straight line graphs, find the gradient and y-intercept, write the equation y = mx + c, and find equations of parallel and perpendicular lines (Higher tier).

What this dot point is asking

WJEC requires you to plot a straight line from its equation or a table of values, to read off and calculate its gradient and y-intercept, to write its equation in the form $y = mx + c$, and at Higher tier to find equations of parallel and perpendicular lines. Straight line graphs connect algebra to geometry and to real-life rates of change, and they reappear in simultaneous equations and inequalities, so confident work with gradient and intercept pays off across the course. They appear on both components.

Plotting a line from its equation

To plot a line, build a small table of values by substituting chosen $x$ values into the equation, then plot the coordinate pairs and join them with a ruled straight line.

For $y = 2x - 1$, substituting $x = 0, 1, 2$ gives $y = -1, 1, 3$, so plot $(0, -1)$, $(1, 1)$ and $(2, 3)$. Three points let you spot a plotting error, since all three should lie on one straight line.

Gradient and intercept

The gradient measures steepness and the intercept fixes the line's height.

A positive gradient rises left to right; a negative gradient falls. A gradient of $3$ means $y$ increases by $3$ for every $1$ that $x$ increases. The intercept is read straight off the graph or from the constant term once the equation is in $y = mx + c$ form.

Writing the equation y = mx + c

Any equation can be put in the form $y = mx + c$ by rearranging so $y$ is alone.

Parallel and perpendicular lines (Higher)

Two lines are parallel when they have the same gradient; only their intercepts differ. So any line parallel to $y = 4x - 1$ has gradient $4$.

Two lines are perpendicular when their gradients multiply to $-1$, which means each gradient is the negative reciprocal of the other. A line perpendicular to $y = 2x + 3$ has gradient $-\tfrac{1}{2}$, because $2 \times -\tfrac{1}{2} = -1$. Combine this with a given point to write the full equation.

Real-life and distance-time graphs

Straight line graphs model real situations where one quantity changes at a steady rate. On a distance-time graph, the gradient is the speed: a steeper line means a faster journey, a horizontal line means stopped, and a line returning to the axis means travelling back. On a conversion graph between two currencies or units, the gradient is the conversion rate. Reading these graphs is really reading a gradient and an intercept in context, so the same $y = mx + c$ thinking applies, with $m$ as the rate and $c$ as the starting value.

Finding the midpoint and using coordinates

WJEC also uses coordinates with straight lines. The midpoint of the segment joining $(x_1, y_1)$ and $(x_2, y_2)$ is $\left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)$, the average of the coordinates. This pairs with the gradient formula and, at Higher, with the length of a segment found by Pythagoras. Together these let you describe a line fully from two points: its gradient, its equation, its midpoint and its length, which links the algebra of $y = mx + c$ to the geometry of the coordinate grid.

Why this matters

Straight line graphs are where algebra becomes visual: a linear equation, a linear sequence and a directly proportional relationship are all the same straight line seen differently. The intersection of two lines is the solution to a pair of simultaneous equations, and a region bounded by lines solves an inequality, so this topic threads through the rest of algebra. WJEC rewards accurate plotting, correct gradient calculation and clear use of $y = mx + c$.