Bellwork Determine whether the ordered pairs are solutions

Bellwork • Determine whether the ordered pairs are solutions of the inequality: 2 x-3 y>-2 • 1. ) (0, 0) • 2. ) (0, 1)

2 x-3 y>-2 • 1. ) (0, 0) is the ordered Pair • 2(0) - 3(0) > -2 • 0 - 0 > -2 • 0 > -2

2 x-3 y>-2 • 1. ) (0, 1) is the ordered Pair • 2(0) - 3(1) > -2 • 0 - 3 > -2 • -3 > -2

Today’s Objective • To be able to graph a linear inequality in two variables.

Recall • Graphing a linear equation in slopeintercept form. • y = mx + b

Finding the slope and intercept y- • Find the Slope and y -intercept of the following equation. • y = 3 x + 2

Finding the slope and intercept y- • When the equation is in the form y = mx + b The slope is m, and the y-intercept is b, So…. . .

y = mx + b • For the • The Slope is 3 equation • y = 3 x + 2 • The y-intercept is 2

Graphing equations in the form y = mx + b Graph the equation y = 3 x+ 2 The y-intercept is 2 The slope is 3 which means the rise is 3 and the run is 1. So….

y = 3 x + 2 y-intercept= 2 Slope = 3 Up 3 and over 1

You Try this one y = -2 x + 3 y-intercept= 3 Down 2 and over 1 Slope = -2

Graph x < -3 & y < 4 Sketch x = -3 and y = 4 x = -3 Now pick a point on one side of the dotted line (0, 0)

Test a Point • Take the point (0, 0) and plug in the x value in x < -3 • x < -3 • 0 < -3 since it’s false, shade the side opposite of (0, 0)….

Graph x < -3 & y < 4 Shade the x = -3 true side & every point on this side solves the inequality.

Graph x < -3 & y < 4 Sketch x = -3 and y = 4 y=4 Now pick a point on one side of the solid line (0, 0)

Test a Point • Take the point (0, 0) and plug in the y value in y < 4 • y < 4 • 0 < 4 since it’s True, shade the side that (0, 0) is on….

Graph x < -3 & y < 4 Shade y = 4 the True Side & every point on this side solves the inequality.

Graph x < -3 & y < 4 y<4 x < -3 What’s the difference between the dotted line and the solid line?

Graph x + y > 3 Sketch y = -x + 3 y= -x +3 Now pick a point on one side of the dotted line (0, 0)

Test a Point • Take the point (0, 0) and plug in the values in y < -x + 3 • y < -x + 3 • 0 < -0 + 3 • 0 < 3 since it’s True, shade the side that (0, 0) is on….

Graph x + y > 3 y= -x +3

You try this one • Graph y < 2 x - 1

Graph y < 2 x - 1 Sketch y = 2 x - 1 y= 2 x - 1 Now pick a point on one side of the dotted line (-1, 0)

Test a Point • Take the point (-1, 0) and plug in the values in y < 2 x - 1 • y < 2 x - 1 • 0 < 2(-1) -1 • 0 < -3 since it’s False, shade the opposite side of (-1, 0).