13.4 – Slope and Rate of Change Slope is a rate of change.
13.4 – Slope and Rate of Change
Slope of any Vertical Line 13.4 – Slope and Rate of Change
Slope of any Horizontal Line 13.4 – Slope and Rate of Change
Find the slope of the line defined by: 13.4 – Slope and Rate of Change
If a linear equation is solved for y, the coefficient of the x represents the slope of the line. Alternative Method to find the slope of a line 13.4 – Slope and Rate of Change
If a linear equation is solved for y, the coefficient of the x represents the slope of the line – Slope and Rate of Change
Parallel Lines are two or more lines with the same slope. These two lines are parallel – Slope and Rate of Change
Perpendicular Lines exist if the product of their slopes is –1. These two lines are perpendicular – Slope and Rate of Change
Are the following lines parallel, perpendicular or neither? NEITHER 13.4 – Slope and Rate of Change
These two lines are perpendicular. Are the following lines parallel, perpendicular or neither? 13.4 – Slope and Rate of Change
For every twenty horizontal feet a road rises 3 feet. What is the grade of the road? 13.4 – Slope and Rate of Change
The pitch of a roof is a slope. It is calculated by using the vertical rise and the horizontal run. If a run rises 7 feet for every 10 feet of horizontal distance, what is the pitch of the roof? 13.4 – Slope and Rate of Change
13.5 – Equations of Lines Slope-Intercept Form– requires the y-intercept and the slope of the line. m = slope of lineb = y-intercept
Slope-Intercept Form: m = slope of lineb = y-intercept 13.5 – Equations of Lines
Slope-Intercept Form: m = slope of lineb = y-intercept 13.5 – Equations of Lines
Slope-Intercept Form: m = slope of lineb = y-intercept 13.5 – Equations of Lines
Write an equation of a line given the slope and the y-intercept – Equations of Lines
Point-Slope Form – requires the coordinates of a point on the line and the slope of the line – Equations of Lines
Point-Slope Form – requires the coordinates of a point on the line and the slope of the line – Equations of Lines
Point-Slope Form – requires the coordinates of a point on the line and the slope of the line – Equations of Lines
Writing an Equation Given Two Points 1. Calculate the slope of the line. 2. Select the form of the equation. a. Standard form b. Slope-intercept form c. Point-slope form 3. Substitute and/or solve for the selected form – Equations of Lines
Writing an Equation Given Two Points or Given the two ordered pairs, write the equation of the line using all three forms. Calculate the slope – Equations of Lines
Writing an Equation Given Two Points Point-slope form 13.5 – Equations of Lines
Writing an Equation Given Two Points Slope-intercept form 13.5 – Equations of Lines
Writing an Equation Given Two Points Standard form LCD: – Equations of Lines
Solving Problems The pool Entertainment company learned that by pricing a pool toy at $10, local sales will reach 200 a week. Lowering the price to $9 will cause sales to rise to 250 a week. a. Assume that the relationship between sales price and number of toys sold is linear. Write an equation that describes the relationship in slope-intercept form. Use ordered pairs of the form (sales price, number sold). b. Predict the weekly sales of the toy if the price is $ – Equations of Lines
Solving Problems 13.5 – Equations of Lines
Solving Problems Predict the weekly sales of the toy if the price is $ – Equations of Lines