2.4 Writing Equations of Lines

2.4 Writing Equations of Lines

Given the Slope and Y-Intercept•Just plug them into y = mx + b

•Example: Write the equation for the line with slope m = 3/2 and y-intercept b = -1

Your Turn!

•Write the equation for the line with m = -1/4 and b = 5

Given a Graph•Find the slope and y-intercept.•Then, plug into y = mx + b

•Example:•Write an equation of the line shown.

Your Turn!

•Write an equation of the line shown.

Point-Slope Form

•y – y1 = m(x – x1)

•Used when you are given:▫The slope and a point▫Two points▫A parallel or perpendicular line and a point

Given the Slope and a Point•Example:•Write an equation of the line through (2,3) with slope of -1/2.

Your Turn!•Write an equation of the line through (-3,4) with slope of 2/3.

Parallel and Perpendicular Lines

•For parallel lines: ▫use the same slope

•For perpendicular lines:▫ use the opposite reciprocal (flip it and change the sign)

•Then use Point-Slope form

Example:•Write an equation of the line that passes through (3, 2) and is parallel to y = -3x + 2.

•Write an equation of the line that passes through (3, 2) and is perpendicular to y = -3x + 2.

Your Turn!•Write an equation of the line that passes through (2, -3) and is parallel to y = 2x – 3.

•Write an equation of the line that passes through (2, -3) and is perpendicular to y = 2x – 3.

Given Two Points

•Find the slope:

•Pick one of the points

•Then use point-slope form (just like with the slope and a point)

Example:

•Write and equation of the line that passes through (-2, -1) and (3, 4).

Your Turn!

•Write and equation of the line that passes through (1, 5) and (4, 2).

stop

Direct Variation

•x and y show direct variation when y = kx and k 0

•k is called the constant of variation

•The graph of y = kx is always a line through the origin (0, 0).

Writing and Using Direct VariationExample:The variables x and y vary directly, and y = 12 when x = 4. ▫Write an equation relating x and y.

▫Find y when x = 5.

Your Turn!The variables x and y vary directly, and y = 15 when x = 3. ▫Write an equation relating x and y.

▫Find y when x = 9.

Identifying Direct Variation

•y = kx can also be written y/x = k

•A set of data pairs (x, y) shows direct variation if y/x is constant.

Example:•Tell whether the data show direct variation. If so, write an equation relating x and y.

14-karat Gold Chains

Length, x (inches)

16 18 20 24 30

Price, y(dollars) 288 324 360 432 540

Your Turn!•Tell whether the data show direct variation. If so, write an equation relating x and y.

Diamonds

Weight, x (carats)

0.5 0.7 1.0 1.5 2.0

Price, y (dollars) 2250 3430 640011,00

020,40

0

Writing Linear Models

•In 1994, Americans purchased an average of 113 meals at restaurants. By 2006, it was 131. Write a linear model for the number of meals purchased per person annually. Use the model to predict how many will be purchased per person in 2016.

Your Turn!

•In 2001, there were 57 million cats as pets in the U.S. By 2008, there were 61 million.

•Write a linear model for the number of cats as pets.

•Use the model to predict the number of cats in 2020.