1. Graph the linear inequality.
y≤4x
2. Graph the linear inequality.
4x+5y≤20
y ≤ 4x
draw a solid straight line y = 4x, then shade in the region below the line
4x + 5y ≤ 20
5y ≤ -4x + 20
y ≤ (-4/5)x + 4
draw a solid straight line y = (-4/5)x + 4 , then shade in the region below the line
To graph linear inequalities, we'll start with the corresponding equations and then modify the graph according to the inequality symbol.
1. Graphing the linear inequality y ≤ 4x:
a) Start by graphing the corresponding equation y = 4x. This is a straight line with a slope of 4 and y-intercept of 0.
b) Since the inequality symbol is "≤", we need to shade the region below the line y = 4x.
c) Draw a dashed line to represent the equation y = 4x, and shade the region below the line to indicate the solutions to the inequality.
Here is the graph:
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2. Graphing the linear inequality 4x + 5y ≤ 20:
a) Start by graphing the corresponding equation 4x + 5y = 20. This is a straight line with a slope of -4/5 and y-intercept of 4.
b) Since the inequality symbol is "≤", we need to shade the region below or on the line 4x + 5y = 20.
c) Draw a solid line to represent the equation 4x + 5y = 20, and shade the region below the line (including the line itself) to indicate the solutions to the inequality.
Here is the graph:
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```
To graph linear inequalities, we need to follow a few steps:
1. Start by graphing the corresponding equality (the line) using the y-intercept and the slope.
2. Determine whether the line is included in the solution set or not.
3. If the line is included, we will use a solid line. If it is not included, we will use a dashed line.
4. Finally, shade the region that satisfies the inequality (above or below the line).
Now let's graph the linear inequalities:
1. y ≤ 4x:
Step 1: Graph the line y = 4x.
- To find the y-intercept, set x = 0. So y = 4(0) = 0.
- To find another point, set x = 1. So y = 4(1) = 4.
Plot these two points (0, 0) and (1, 4) on the coordinate plane and draw a line passing through them.
Step 2: Determine if the line is included. In this case, since the inequality is y ≤ 4x, the line is included.
Step 3: Use a solid line to represent the line y = 4x.
Step 4: Shade the region below the line since y is less than 4x.
The final graph will have a solid line passing through (0, 0) and (1, 4), with the region below the line shaded.
2. 4x + 5y ≤ 20:
Step 1: Graph the line 4x + 5y = 20.
- To find the x-intercept, set y = 0. So 4x + 5(0) = 20, which gives x = 5.
- To find the y-intercept, set x = 0. So 4(0) + 5y = 20, which gives y = 4.
Plot these two points (5, 0) and (0, 4) on the coordinate plane and draw a line passing through them.
Step 2: Determine if the line is included. In this case, since the inequality is 4x + 5y ≤ 20, the line is included.
Step 3: Use a solid line to represent the line 4x + 5y = 20.
Step 4: Shade the region below the line since 4x + 5y is less than or equal to 20.
The final graph will have a solid line passing through (5, 0) and (0, 4), with the region below the line shaded.