SWBAT calculate the gradient, intercepts, equation of a 2D line, and find a point of intersection in

writing from two pointsDO Now:

Gradient

• GRADIENT is the way we say SLOPE (m)– Definition:• The constant rate of change • The ratio of the change in dependent variable to the

change of the independent variable

m=

Gradient from a Graph

• Find two points ON THE LINE!– For best results, try to choose points that have

integer coordinates (where the gridlines meet)A) Method 1: Draw a right triangle from the one

point to the next and count the spaces for each variable.

B) Method 2: Use the formula to calculate the slope more accurately from the coordinates of both points.

Gradient from a Table

• Determine the change in the dependent variable = Δy

• Determine the change in the independent variable = Δx

• Divide to determine the ratio

Gradient from Two Points

• Label the coordinates x1,y1 and x2,y2

• Write the gradient formulam=

• Substitute the known values into the formula• Solve! (remember units if there are any!)

Special Gradients

• Zero Gradient: m = = 0– Signifies a horizontal line

• Undefined Gradient: m = = No slope!– Signifies a vertical line

• Same Gradient: Two lines with same gradient are either parallel lines or same line.

• Negative Reciprocal: Two lines are negative reciprocals of each other are perpendicular

Homework:

• P. 90 Exercise 3A• P. 91 Exercise 3B (2-4)• P. 92 Exercise 3C• P. 94 Exercise 3D (2, 3, 4, 6, 7)