Chapter 2 Section 3: Quick Graphs of Linear Equations Section 4: Writing Equations of Lines

There are 4 ways to represent any function and 3 ways to write an equation of a line.

There are 4 ways to represent any function: G raphically/visual N umerically/table A nalytically/equation W ords/verbally

There are 3 ways to write an equation of a line: lope-Intercept Form P oint-Slope Form S tandard Form

Open to p. 82 Complete the activity and turn it in

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

Graph the equations using the slope-intercept form. b =

Graph the equations using the slope-intercept form. b =

Graph the equations using the slope-intercept form. b =

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.

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)

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).

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).

( , 0) (0, )

( , 0) (0, )

( , 0) (0, )

USING STANDARD FORM The school band is selling sweatshirts and T-shirts to raise money. The goal is to raise $1200. 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

WRITING AN EQATION OF A LINE

SLOPE-INTECEPT FORM Given the slope m and the y-intercept b use the equation: y = mx +b

POINT-SLOPE

FORM Given slope m and a point (x1, y1), use this equation: y – y1 =m(x – x1)

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.

WRITING AN EQUATION GIVEN THE SLOPE AND Y-INTERCEPT

4. m = -3 and b = 6 5. m = and b = -8 6. m = 4 and b = 3

WRITING AN EQUATION GIVEN THE SLOPE AND POINT

7. Write an equation of the line that passes through (2, 3) and has a slope of .

SLOPE-INTERCEPT FORM

8. Write an equation of the line that passes through (5, 4) and has a slope of -3.

SLOPE-INTERCEPT FORM

WRITING EQUATIONS OF PERPENDICULAR AND PARALLEL LINES

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

PERPENDICULAR PARALLEL

Write an equation of a line that passes through (-2, 3) and is (a) perpendicular and (b) parallel to the line y = -4x + 1.

PERPENDICULAR PARALLEL

WRITING AN EQUATION GIVEN TWO POINTS

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

SLOPE-INTERCEPT FORM

12. Write an equation of the line that passes through (5, -2) and (2, 10).

SLOPE-INTERCEPT FORM

WRITING DIRECT VARIATON EQATIONS

DIRECT VARIATION EQUATION y = kx and k 0.

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.

WRITING AND USING A DIRECT VARIATION EQUATION

The variables x and y vary directly, and y = 12 and x = 4.

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.

The variables x and y vary directly, and y = 8 and x = -4.

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.

IDENTIFYING DIRECT VARIATION

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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