NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3.

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NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Slope-Intercept Form (of a line) Where m is the slope (in the form of a fraction) b is the y-intercept x & y are points on the line in the form (x, y)

Example 4-1a Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Answer: The slope-intercept form of the equation of the line is Slope-intercept form

Write an equation in slope-intercept form of the line with slope of –1 and y-intercept of 4. Your Turn:

Point-Slope Form (of a line) Where: And (x, y) never get replaced.

Example 4-2a Answer: Write an equation in point-slope form of the line whose slope is that contains (–10, 8). Simplify. Point-slope form

Write an equation in point-slope form of the line whose slope is that contains (6, –3). Your Turn:

Example 4-3a 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 4-3b Now use the slope-intercept form and either point to write an equation. Slope-intercept form Fill in m & b. Using (4, 9): Solve for b

Example 4-3c OR Using (–2, 0): Answer: Slope-intercept form Fill in m & b. Solve for b (–2, 0)

Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8). Answer:

Write an equation in slope-intercept form for a line containing (-2, 4) and (6, -2). Answer:

Write an equation in slope-intercept form for a line containing (-2, 4) and (-2, -2).

Example 4-4a 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. Slope-intercept form Fill in m & b. Solve for b

Write an equation in slope-intercept form for a line containing (4, 1) that is perpendicular to the line Your turn: Answer:

Example 4-5a 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. Answer: The total annual cost can be represented by the equation Slope-intercept form

Example 4-5b 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.

Example 4-5d Answer: RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit. a. Write an equation to represent the total cost C for d days of use. b. Compare this rental cost to a company which charges a $50 deposit but $35 per day for use. If a person expects to rent a car for 9 days, which company offers the better rate? Answer: The first company offers the better rate. Nine days cost $325 instead of $365.