Sketching linear graphs using the gradient and y-intercept:

In linear equations in the form y = mx + b

m is the gradient

b is the y intercept

Sketching linear graphs that pass through the origin:

Graphs that pass through the origin are in the form

y = mx

Here, the y intercept is the origin (0,0)

m is the gradient

Sketching parallel lines:

Two lines with the same gradient are parallel lines.

Conversely, parallel lines have the same gradient.

Sketching perpendicular lines:

The products of the gradients of two perpendicular lines is equal to -1.

Conversely, if the products of the gradients of two lines is -1, then the lines are perpendicular.

Sketching linear graphs using x and y intercepts:

To find the x-intercept, substitute y=0 into the equation.

To find the y-intercept, substitute x=0 into the equation.

Sketching vertical and horizontal graphs:

Equations of the form y=b are straight lines parallel to the x-axis (horizontal lines)

Equations of the form x=a are straight lines parallel to the y-axis (vertical lines).

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