Warm up: Positive SlopeNegative SlopeSlope of 0 No Slope Section 2.1 – Linear Equations in Two Variables Based upon each graph below, identify the slope as positive, negative, zero, or no slope/undefined. y = mx + b m is positive y = -mx + b m is negative y = k m is zero x = k m is undefined

Section 2.1 – Linear Equations in Two Variables After this section you should be able to: Calculate the slope of a line given two points. Write the equation of a line (in Point – Slope Form). Write the equation of a line (in Standard Form). Ax+By = C Solve real-world problems using linear equations. Use slope to identify parallel and perpendicular lines

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

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

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) Write the equation of a line (in Point – Slope Form)

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 Standard Form (Ax + By = C).

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 $28,500 in 1998 and $32,900 in If your salary follows a linear growth pattern, what will your salary be in 2003? (1998, 28,500) (2000, 32,900) (2003, ???) Use your equation to predict the salary for 2003 x = y = year salary Use your equation to predict the salary for 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) x = y = years since purchasing Value (V) This equation represents Value (V)

A contractor purchases a piece of equipment for $36,500. The equipment requires an average expenditure of $5.25 per hour for fuel and maintenance, and the operator is paid $11.50 per hour. a)Write a linear equation giving the total cost C of operating this equipment for t hours. b)Assuming that customers are charged $27 per hour of machine use, an equation which represents the profit. c) Find the ‘break-even’ point.

Section 2.1 – Linear Equations in Two Variables After this section you should be able to: Calculate the slope of a line given two points. Write the equation of a line (in Point – Slope Form). Write the equation of a line (in Standard Form). Ax+By = C Solve real-world problems using linear equations. Homework: Pg. 181 #29, 30, 33, (74-75 standard form), 78, 79 Use slope to identify parallel and perpendicular lines Quiz 2.1 FRIDAY