y = mx + c

Understanding y = mx + c

Basic Concept

• The equation y = mx + c is the general equation of a straight line.
• In this equation, ‘y’ and ‘x’ are the coordinates of any point on the line.
• ‘m’ represents the gradient of the line.
• ‘c’ refers to the y-intercept, or where the line crosses the y-axis.

Gradient ‘m’

• The gradient ‘m’ is a measure of the steepness of the line.
• A positive gradient means the line slopes upwards from left to right.
• A negative gradient indicates the line slopes downwards, again from left to right.
• Horizontal lines have a gradient of 0, while vertical lines have an undefined gradient.

Y-intercept ‘c’

• The y-intercept ‘c’ is the ‘y’ coordinate where the line crosses the y-axis.
• Specifically, it’s the value of ‘y’ when ‘x’ is 0.

Plotting the Line

• Begin plotting the line ‘y = mx + c’ by marking the y-intercept ‘c’ on the y-axis.
• Then use the gradient ‘m’ to find another point on the line: moving one step right and ‘m’ steps up (or down if ‘m’ is negative).
• Draw the line through these points.

Applying y = mx + c

Determining the Equation of a Line

• To derive the equation of a straight line, you need to know the gradient and either the y-intercept or a point on the line.
• Given the gradient and a point on the line (x1, y1), you can solve for ‘c’ by rearranging the equation y = mx + c to c = y - mx and substituting the known values.

Interpreting the Equation

• The values of ‘m’ and ‘c’ in the equation y = mx + c tell us about the line.
• A higher absolute value of ‘m’ indicates a steeper slope.
• A higher value of ‘c’ indicates that the line crosses the y-axis higher up.
• Reading graphs and understanding these values can help in solving a variety of mathematical problems.