Section 2.1 – Linear Equations in Two Variables

Match the graph with the appropriate slope: No Slope (undefined) Zero Slope Positive Slope Negative Slope 1 2 3 4 C D B A

Based upon each graph below, identify the slope as positive, negative, zero, or no slope/undefined. 1 2 3 4 positive zero undefined negative 5 6 7 8 zero undefined negative positive

Comment on the equation of the line given the graph: 1 2 3 4 y = mx + b m is positive y = mx + b m is negative y = k m is zero x = k m is undefined

Comment on the equation of the line given the graph below: 1 2 3 4 y = mx +b m is positive y = k m is zero x = k m is undefined y = mx + b m is negative 5 6 7 8 y = k m is zero x = k m is undefined y = mx + b m is negative y = mx +b m is positive

Find the slope of the line given the two points Comment briefly on the graph of the line connecting the two points. (up to the right, down to the right, vertical, or horizontal) (2, 0), (8, 12) graph is up to right graph is up to right Vertical; x = 5

Find the slope of the line given the two points Comment briefly on the graph of the line connecting the two points. (up to the right, down to the right, vertical, or horizontal) (-1, 5), (2, 4) Horizontal y = -3 graph is down to right Vertical x = 5

ALL Equations – Point Slope Form Find the equation of the line which passes through (2, 3) and (3, 5) Find the equation of the line which passes through (3, 0) and (3, 3) Find the equation of the line which passes through (6, 7) and (2, 7)

Find the equation of the line with slope 5 passing through (3, -1) Find the equation of the line passing through (2, 3) and (7, 5) Find the equation of the line passing through (4, 6) and (4, -1)

Parallel Lines – Same Slope Normal Lines – Negative/Reciprocal Slopes Determine if the lines connecting the two points below are parallel, perpendicular, or neither. neither Determine if the lines connecting the two points below are parallel, perpendicular, or neither. perpendicular

Find the equation of the line parallel to 2x – 5y = -3 which passes through (3, 1). Rewrite your equation in Ax + By = C form.

Find the equation of the line perpendicular to 7x – y = 4 which passes through (2, -5). Rewrite your equation in Ax + By = C form.

Your salary was $28500 in 1998 and $32900 in 2000. If your salary follows a linear growth pattern, what will your salary be in 2003?

A business purchases a piece of equipment for $875. After 5 years the equipment will be outdated and have no value. Write a linear equation giving the value V of the equipment during the 5 years it will be used. (0, 875) and (5, 0)

A contractor purchases a piece of equipment for $36500. The equipment requires an average expenditure of $5.25 per hour for fuel and maintenance, and the operator is paid $11.50 per hour. Write a linear equation giving the total cost C of operating this equipment for t hours. Assuming that customers are charged $27 per hour of machine use, an equation which represents the profit. c) Find the ‘break-even’ point.