y= mx + c

Understanding the Equation of a Line: y = mx + c

Basics of y = mx + c

The equation y = mx + c describes a straight line in the cartesian coordinate system.
It’s known as the slope-intercept form of the line equation.
In this equation, m represents the slope or gradient of the line, c is the y-intercept, where the line crosses the y-axis.

Using the Slope (m)

The slope, m, dictates the direction and steepness of the line. If m is positive, the line rises from left to right. If m is negative, the line falls from left to right.
A larger absolute value of m suggests a steeper slope—it either increases or decreases more rapidly. A smaller absolute value suggests a gentler slope—it either increases or decreases more slowly.
A slope of 0 indicates a flat, horizontal line.

Understanding the Y-intercept (c)

The y-intercept, c, is the point where the line crosses the y-axis. It’s the value of y when x is 0.
A larger c moves the line upwards, whereas a smaller c (including negatives) moves the line downwards.

Applying y = mx + c in Problem-Solving

Drawing Lines from Equations

When asked to draw a line from an equation in form y = mx + c, first locate the y-intercept on the y-axis and plot it. Then, use the slope to find another point on the line (rise/run method). Draw a straight line through these points extending in both directions.

Finding Equations from Lines

To find the equation of a line from a graph, first identify the y-intercept (c) and then determine the slope (m) between two points of the line. Plug these values into the y = mx + c formula.

Remember, y = mx + c is fundamental to understanding linear relationships in Algebra, and this formula has far-reaching applications in higher levels of Maths and Science. Practise graphing and finding equations to build fluency with these skills.