Lesson 2: 4-2 Writing Equations in Standard and Point-Slope Forms
Duration of Days: 5
Lesson Objective
Write equations of lines in standard form and point-slope form.
Write linear equations in different forms.
How is point-slope form related to the formula for slope?
How can you use the point-slope form of a line to graph the line?
A.CED.2 Create equations in two or more variables and represent relationships between quantities; graph equations on coordinate axes with labels and scales.
SAT questions related to writing equations: 5-4-11,4-3-8,8-4-7,1-3-12,7-3-19
functions: 8-4-4, 7-4-18, 8-4-18, 2-4-14, 3-4-20, 1-4-5, 7-4-21,
Solving Equations: 5-3-17, 6-4-32, 3-4-7, 8-3-1, 3-3-17, 6-3-17, 1-3-1, 3-3-2, 2-3-1, 7-3-16, 6-3-6,
Point-slope form is derived from the definition of slope. Suppose two points on a line are given as (x, y) and (x1, y1). Using the definition of slope, m = y - y1 / x - x1 , if each side of the equation is multiplied by (x - x1), the result is y - y 1 = m (x - x1), the point-slope form of a linear equation.
Most humane societies have foster homes for newborn puppies, kittens and injured or sick animals. During the spring and summer, a large shelter can place 3000 animals in homes each month.
If a shelter had 200 animals in foster homes at the beginning of spring, y = 3000x + 200 could be used to represent the number of amimals placed in foster homes y after x months.
Emphasize that in standard form, A, B, and C are all integers. Example 3 is an exercise in algebraic manipulation.
If students have trouble remembering whether a vertical line or a horizontal line has slope 0, then tell them the word horizontal has an o to remind them of 0. A horizontal line has slope 0. Challenge students to create a catchy phrase to help them remember the different forms for a linear equation.
Extension: Write 4x + 3y = 8 on the board. Ask students to rewrite the equation in slope-intercept form. Have students name the slope and then draw a conclusion about the relationship between the slope and values of A and B when an equation is written in standard form, Ax + By = C.
Practice: Exercises 1 - 12
Exercises 48-55
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