Graphing Linear Functions 1 graph linear functions 2

Graphing Linear Functions 1. graph linear functions. 2. write equations in standard form.

Warm Up, Do Now! • Solve for y 1. 3 – y = 10 2. 2 y + 4 = 8 3. 9 y + (-1) = 8 4. 0 – 5 = -10 y

Practice 1) Solve for y: 2) Solve for y: 3) Solve for y: 2 x + y = 4 4 x + 2 y = -6 x – 3 y = 6 Solve for y means isolate y. Get y all by itself!

1) Review: Solve for y • • Draw “the river” Subtract 2 x from both sides 2) Solve for y: • • 2 x + y = 4 - 2 x y = -2 x + 4 4 x + 2 y = -6 - 4 x Subtract 4 x 2 y = -4 x - 6 Simplify Divide both sides by 2 2 2 Simplify y = -2 x - 3

3) Solve for y: • • x - 3 y = 6 x x Subtract x Simplify -3 y = -x + 6 Divide both sides by -3 -3 -3 Simplify or

Graphing Steps 1) Isolate the variable (solve for y). 2) Make a t-table. If the domain is not given, pick your own values. 3) Plot the points on a graph. 4) Connect the points.

Make a t-table If f(x) = 2 x + 4, complete a table using the domain {-2, -1, 0, 1, 2}. x -2 -1 0 1 2 f(x) ordered pair 2(-2) + 4 = 0 (-2, 0) 2(-1) + 4 = 2 (-1, 2) 2(0) + 4 = 4 (0, 4) 2(1) + 4 = 6 (1, 6) 2(2) + 4 = 8 (2, 8)

1) Given the domain {-2, -1, 0, 1, 2}, graph 3 x + y = 6 • Solve for y: Subtract 3 x 2. Make a table x -3 x + 6 -2 -3(-2) + 6 = 12 -1 -3(-1) + 6 = 9 0 -3(0) + 6 = 6 1 -3(1) + 6 = 3 2 -3(2) + 6 = 0 3 x + y = 6 - 3 x y = -3 x + 6 ordered pair (-2, 12) (-1, 9) (0, 6) (1, 3) (2, 0)

1) Given the domain {-2, -1, 0, 1, 2}, graph 3 x + y = 6 • Plot the points (-2, 12), (-1, 9), (0, 6), (1, 3), (2, 0) • Connect the points. Bonus questions! What is the x-intercept? (2, 0) What is the y-intercept? (0, 6) Does the line increase or decrease? Decrease

Ex. 2) Which is the graph of = x – 4? 1. 2. 3. 4. . . y

Standard Form Ax + By = C A, B, and C have to be integers An equation is LINEAR (the graph is a straight line) if it can be written in standard form.

Determine whether each equation is a linear equation. 3) 4 x = 7 + 2 y Can you write this in the form Ax + By = C? 4 x - 2 y = 7 A = 4, B = -2, C = 7 This is linear!

Determine whether each equation is a linear equation. 4) 2 x 2 - y = 7 Can you write it in standard form? NO - it has an exponent! Not linear 5) x = 12 x + 0 y = 12 A = 1, B = 0, C = 12 Linear

Here’s the cheat sheet! An equation that is linear does NOT contain the following: 1. Variables in the denominator 2. Variables with exponents 3. Variables multiplied with other variables. xy = 12

Is this equation linear? 1. Yes 2. No Standard Form x – 4 y = 3

Is this equation linear? 1. Yes 2. No Exponents are not allowed!

Is this equation linear? y = -3 1. Yes 2. No Standard Form 0 x + y = -3

x and y -intercepts ● The x-intercept is the point where a line crosses the x-axis. The general form of the x-intercept is (x, 0). The y-coordinate will always be zero. ● The y-intercept is the point where a line crosses the y-axis. The general form of the y-intercept is (0, y). The x-coordinate will always be zero.

To find intercepts…. ● To find the x-intercept, plug in 0 for y. ● To find the y-intercept, plug in 0 for x.

Find the x and y- intercepts of x = 4 y – 5 ● x-intercept: ● Plug in y = 0 x = 4 y - 5 x = 4(0) - 5 x=0 -5 x = -5 ● (-5, 0) is the x-intercept ● y-intercept: ● Plug in x = 0 x = 4 y - 5 0 = 4 y - 5 5 = 4 y =y ● (0, ) is the y-intercept

Find the x and y-intercepts of g(x) = -3 x – 1* ● x-intercept ● Plug in y = 0 g(x) = -3 x - 1 0 = -3 x - 1 1 = -3 x =x ● ( , 0) is the x-intercept *g(x) is the same as y ● y-intercept ● Plug in x = 0 g(x) = -3(0) - 1 g(x) = 0 - 1 g(x) = -1 ● (0, -1) is the y-intercept

Find the x and y-intercepts of 6 x - 3 y =-18 ● x-intercept ● Plug in y = 0 6 x - 3 y = -18 6 x -3(0) = -18 6 x - 0 = -18 6 x = -18 x = -3 ● (-3, 0) is the x-intercept ● y-intercept ● Plug in x = 0 6 x -3 y = -18 6(0) -3 y = -18 0 - 3 y = -18 -3 y = -18 y=6 ● (0, 6) is the y-intercept

Find the x and y-intercepts of x = 3 ● x-intercept ● ● Plug in y = 0. ● There is no y. Why? x = 3 is a vertical line so x always equals 3. ● ● y-intercept A vertical line never crosses the y-axis. ● There is no y-intercept. (3, 0) is the x-intercept. x

Find the x and y-intercepts of y = -2 ● x-intercept ● y-intercept ● Plug in y = 0. ● y = -2 is a horizontal line y cannot = 0 because y = -2. ● y = -2 is a horizontal line so it never crosses the x-axis. ●There so y always equals -2. ● (0, -2) is the y-intercept. x is no x-intercept. y

Graphing Equations ● Example: Graph the equation -5 x + y = 2 Solve for y first. -5 x + y = 2 Add 5 x to both sides y = 5 x + 2 ● The equation y = 5 x + 2 is in slope-intercept form, y = mx+b. The y-intercept is 2 and the slope is 5. Graph the line on the coordinate plane.

Graphing Equations Graph y = 5 x + 2 x y

Graphing Equations Graph 4 x - 3 y = 12 ● Solve for y first 4 x - 3 y =12 Subtract 4 x from both sides -3 y = -4 x + 12 Divide by -3 y= x+ Simplify y= x– 4 ● The equation y = x - 4 is in slope-intercept form, y=mx+b. The y -intercept is -4 and the slope is. Graph the line on the coordinate plane.

Graphing Equations Graph y = x - 4 x y