graph the following linear equations and determine the correct classification:
L1:y=-x+5 and L2:y=-2x+1
a flagpole casts a shadow 10 ft. long if a man 6 ft. tall casts a shadow 4 ft. long at the same time of day, how tall is the flagpole.
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Let x = length of flagpole.
x/10 = 6/4
Solve for x.
To graph the linear equations and determine their classification, we will follow these steps:
Step 1: Plotting the graphs:
For each equation, we need to find two points and then connect them to form a straight line. To find the points, we can assign values to either x or y and solve for the other variable. Let's find two points for each equation:
Equation 1: L1: y = -x + 5
When x = 0, y = -0 + 5 = 5
When x = 5, y = -5 + 5 = 0
So, our two points for L1 are (0, 5) and (5, 0).
Equation 2: L2: y = -2x + 1
When x = 0, y = -2(0) + 1 = 1
When x = 3, y = -2(3) + 1 = -5
So, our two points for L2 are (0, 1) and (3, -5).
Step 2: Graphing the lines:
Now, let's plot the points we found for each equation on a coordinate plane and draw lines connecting them.
For L1, we plot the points (0, 5) and (5, 0) and draw a line passing through them.
For L2, we plot the points (0, 1) and (3, -5) and draw a line passing through them.
Step 3: Classifying the lines:
To determine the classification of the lines, we need to compare their slopes.
L1 has a slope of -1, which is a negative slope.
L2 has a slope of -2, which is also a negative slope.
Since both slopes are negative, we can classify both lines as "decreasing" or "downward sloping" lines.
Visually inspecting the graph, the lines L1 and L2 will be lines sloping downwards from left to right.
Note: The classification of a line as "increasing" or "decreasing" depends on the slope value. If the slope is positive, the line will be increasing, and if the slope is negative, the line will be decreasing.