Coordinate Geometry: Equation of a Straight Line

Front

What is the gradient of a straight line?

Back

The gradient (or slope) of a straight line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

How do you find the equation of a line in the form y=mx+c?

Back

To find the equation of a line in the form y=mx+c, identify the gradient (m) and the y-intercept (c) from a graph or two points on the line.

Front

What does the y-intercept of a line represent?

Back

The y-intercept of a line is the point where the line crosses the y-axis, represented as (0, c) in the equation y=mx+c.

Front

What is the significance of a negative gradient?

Back

A negative gradient indicates that as the x-value increases, the y-value decreases, meaning the line slopes downwards from left to right.

Front

How can you determine the y-intercept from the equation of a line?

Back

In the equation y=mx+c, the y-intercept is the value of c.

Front

What is the formula to calculate the gradient between two points (x1, y1) and (x2, y2)?

Back

The gradient (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a line is vertical?

Back

A vertical line has an undefined gradient and can be represented by the equation x = a, where 'a' is a constant.

Front

What does it mean if a line is horizontal?

Back

A horizontal line has a gradient of 0 and can be represented by the equation y = b, where 'b' is a constant.

Front

How do you identify the gradient from a graph?

Back

The gradient can be identified by selecting two points on the line and calculating the rise over run between them.

Front

What is the equation of a line that intercepts the y-axis at 5?

Back

The equation of a line that intercepts the y-axis at 5 can be written as y = mx + 5, where m is the gradient.