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Chapter 2 Section 3: Quick Graphs of Linear Equations
Section 4: Writing Equations of Lines
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There are 4 ways to represent any function and 3 ways to write an equation of a line.
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There are 4 ways to represent any function:
G raphically/visual N umerically/table A nalytically/equation W ords/verbally
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There are 3 ways to write an equation of a line:
lope-Intercept Form P oint-Slope Form S tandard Form
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Open to p. 82 Complete the activity and turn it in
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GRAPHING WITH THE SLOPE-INTERCEPT FORM
m = slope and b = y-intercept; (0, b) Plot the point where the line crosses the y-axis Find the slope and use it to plot the 2nd point Draw a line through the two points
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Graph the equations using the slope-intercept form.
b =
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Graph the equations using the slope-intercept form.
b =
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Graph the equations using the slope-intercept form.
b =
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USING THE SLOPE-INTERCEPT FORM
You are buying an $1100 computer on layaway. You make a $250 deposit and then make weekly payments according to the equation a = 850 – 50t where a is the amount you owe and t is the number of weeks. a. What is the original amount you owe on layaway? b. What is your weekly payment? c. Graph the model.
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GRAPHING HORIZONTAL AND VERICAL LINES
HORIZONTAL AND VERTICAL LINES Horizontal Lines: The graph of y = c is a horizontal line through (0, c) Vertical Lines: The graph of x = c is a vertical line through (c, 0)
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P86#21-57x3 to be turned in Thur.
How many points are required to graph a line? What if the equation is not in slope-intercept form, but is in standard form? Easiest way to graph in standard form is to graph the x-intercept (x, 0) and y-intercept (0, b).
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GRAPHING WITH STANDARD FORM
A and B are not zero Easiest way to graph in standard form is to graph the x-intercept (x, 0) and y-intercept (0, b).
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( , 0) (0, )
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( , 0) (0, )
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( , 0) (0, )
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USING STANDARD FORM The school band is selling sweatshirts and T-shirts to raise money. The goal is to raise $ Sweatshirts sell for a profit of $2.50 each and T-shirts for $1.50 each. Describe the numbers of sweatshirts and T-shirts the band can sell to reach the goal. 2.5s+1.5t=1200 Graph the model
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WRITING AN EQATION OF A LINE
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SLOPE-INTECEPT FORM Given the slope m and the y-intercept b use the equation: y = mx +b
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POINT-SLOPE
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FORM Given slope m and a point (x1, y1), use this equation: y – y1 =m(x – x1)
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TWO POINTS Given two points (x1, y1) and (x2, y2), use the formula: t find the slope m. Then use the slope-intercept form or point-slope form with the slope and either point of the given points to write an equation of a line.
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WRITING AN EQUATION GIVEN THE SLOPE AND Y-INTERCEPT
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4. m = -3 and b = 6 5. m = and b = -8 6. m = 4 and b = 3
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WRITING AN EQUATION GIVEN THE SLOPE AND POINT
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7. Write an equation of the line that passes through (2, 3) and has a slope of .
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SLOPE-INTERCEPT FORM
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8. Write an equation of the line that passes through (5, 4) and has a slope of -3.
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SLOPE-INTERCEPT FORM
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WRITING EQUATIONS OF PERPENDICULAR AND PARALLEL LINES
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Write an equation of a line that passes through (3, 2) and is (a) perpendicular and (b) parallel to the line y = -3x + 2.
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PERPENDICULAR PARALLEL
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Write an equation of a line that passes through (-2, 3) and is (a) perpendicular and (b) parallel to the line y = -4x + 1.
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PERPENDICULAR PARALLEL
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WRITING AN EQUATION GIVEN TWO POINTS
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Write an equation of the line that passes through (-2, -1) and (3, 4).
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SLOPE-INTERCEPT FORM
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12. Write an equation of the line that passes through (5, -2) and (2, 10).
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SLOPE-INTERCEPT FORM
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WRITING DIRECT VARIATON EQATIONS
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DIRECT VARIATION EQUATION y = kx and k 0.
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The nonzero constant k is called constant of variation and y is said to vary directly with x. The graph of y = kx is a line through the origin.
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WRITING AND USING A DIRECT VARIATION EQUATION
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The variables x and y vary directly, and y = 12 and x = 4.
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13a. Write and graph an equation relating x and y. 13b
13a. Write and graph an equation relating x and y. 13b. Find y when x = 5.
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The variables x and y vary directly, and y = 8 and x = -4.
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14a. Write and graph an equation relating x and y. 14b
14a. Write and graph an equation relating x and y. 14b. Find x when y = 2.
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IDENTIFYING DIRECT VARIATION
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Tell whether the data show direct variation
Tell whether the data show direct variation. If so, write an equation relating and y.
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14-Karot Gold Chains (1 gram/in)
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Length, x (in)
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Price, y ($)
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Loose Diamonds (round, colorless, very small flaws)
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Weight, x (Carats)
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Price, y ($) ,000 20,4000
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