For the equation $-5x - 4y = 20$:
a) Complete the table.
b) Plot the two points you found in the table.
Answer (2)
Substitute x = 0 into the equation − 5 x − 4 y = 20 and solve for y , resulting in the point ( 0 , − 5 ) .
Substitute x = − 4 into the equation − 5 x − 4 y = 20 and solve for y , resulting in the point ( − 4 , 0 ) .
The two points that satisfy the equation are ( 0 , − 5 ) and ( − 4 , 0 ) .
These points can be plotted on a coordinate plane. The points are ( 0 , − 5 ) and ( − 4 , 0 ) .
Explanation
Understanding the Problem We are given the equation − 5 x − 4 y = 20 and asked to complete a table of values and plot the corresponding points. To complete the table, we need to find two points (x, y) that satisfy the equation.
Finding the First Point Let's choose x = 0 . Substituting this into the equation, we get: − 5 ( 0 ) − 4 y = 20
− 4 y = 20
y = − 4 20 = − 5
So, when x = 0 , y = − 5 . This gives us the point ( 0 , − 5 ) .
Finding the Second Point Now, let's choose x = − 4 . Substituting this into the equation, we get: − 5 ( − 4 ) − 4 y = 20
20 − 4 y = 20
− 4 y = 0
y = − 4 0 = 0
So, when x = − 4 , y = 0 . This gives us the point ( − 4 , 0 ) .
Summary of Points We have found two points that satisfy the equation: ( 0 , − 5 ) and ( − 4 , 0 ) . These points can now be plotted on a coordinate plane.
Final Answer The two points we found are ( 0 , − 5 ) and ( − 4 , 0 ) .
Examples
Linear equations are used in various real-life scenarios, such as determining the cost of items, calculating distances, and modeling relationships between two variables. For example, if a taxi charges a fixed fee plus a per-mile rate, the total cost can be modeled using a linear equation. Understanding how to find points on a line helps in predicting outcomes and making informed decisions in these situations.
We found two points that satisfy the equation − 5 x − 4 y = 20 : ( 0 , − 5 ) and ( − 4 , 0 ) . These points can be plotted on the coordinate plane. The first point is on the y-axis, while the second point is on the x-axis.
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