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 y-intercept
•Find the Slope and y-intercept of the following equation. • y = 3x + 2
Finding the slope and y-intercept
•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 = 3x + 2 •The y-intercept
is 2
Graphing equations in the form y = mx + b Graph the equation y = 3x+ 2 The y-intercept is 2 The slope is 3 which means the rise is 3 and the run is 1. So….
y = 3x + 2
Slope = 3
y-intercept= 2
Up 3 and over 1
You Try this one y = -2x + 3
y-intercept= 3
Slope = -2
Down 2 and over 1
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 xside & = -3 true 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 4 True Side & every y = the 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 < 2x - 1
Graph y < 2x - 1 Sketch y = 2x - 1
y= 2x - 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 < 2x - 1
• y < 2x - 1 • 0 < 2(-1) -1 • 0 < -3
since it’s False, shade the opposite side of (-1,0).
Graph y > 2x - 1
y= 2x - 1