3.4 Equations of Lines.

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Presentation transcript:

3.4 Equations of Lines

Objectives Write an equation of a line given information about its graph Solve problems by writing equations

Equations of Lines Equations of lines can be written given any of the following: The slope and y-intercept The slope and the coordinates of a point on the line The coordinates of two points on the line

Slope – Intercept Form y = mx + b Equations of Lines Slope – Intercept Form y = mx + b Point – Slope Form y – y1 = m(x – x1)

Example 1: Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Slope-intercept form Answer: The slope-intercept form of the equation of the line is

Example 2: Write an equation in point-slope form of the line whose slope is that contains (–10, 8). Point-slope form Simplify. Answer:

Example 3: Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0). Find the slope of the line. Slope formula Simplify.

Example 3: Now use the point-slope form and either point to write an equation. Using (4, 9): Point-slope form Distributive Property Add 9 to each side.

Example 3: Using (–2, 0): Point-slope form Simplify. Distributive Property Answer:

Example 4: the slope of a line perpendicular to it is 2. Write an equation in slope-intercept form for a line containing (1, 7) that is perpendicular to the line the slope of a line perpendicular to it is 2.

Example 4: Point-slope form Distributive Property Add 7 to each side. Answer:

Example 5a: RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Write an equation to represent the total annual cost A for r months of rent. For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750. Slope-intercept form Answer: The total annual cost can be represented by the equation

Example 5b: RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Compare this rental cost to a complex which charges a $200 security deposit but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate? First complex: Second complex: Simplify. Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.

Assignment Pre-AP Geometry: Pg. 148 #16 - 44 evens