Question
Graph the equation ![Y equals negative 4 x plus 3](data:image/png;base64,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)
Hint:
To plot the graph of an equation, first we make a table of points satisfying that equation. Then we draw an x-axis and y-axis on the graph. After that we scale both the axis according the values we get in the table. Lastly, we plot the points from the table on the graph and join them to get the required curve.
The correct answer is: After plotting the points, we join them with a line to get the graph of the equation.
Step by step solution:
The given equation is
y = -4x + 3
First we make a table of points satisfying the equation.
Putting x = 0 in the above equation, we will get, y = 3
Similarly, putting x = 1 , in the above equation, we get y = -1
Continuing this way, we have
For x = -1, we get y = 7
For x = 2, we get y = -5
For x = -2, we get y = 11
Making a table of all these points, we have
![](data:image/png;base64,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)
Now we plot these points on the graph.
![](data:image/png;base64,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)
After plotting the points, we join them with a line to get the graph of the equation.
First we make a table of points satisfying the equation.
Putting x = 0 in the above equation, we will get, y = 3
Similarly, putting x = 1 , in the above equation, we get y = -1
Continuing this way, we have
Making a table of all these points, we have
Now we plot these points on the graph.
After plotting the points, we join them with a line to get the graph of the equation.
We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. This makes plotting the graph simpler. We can also find the values by putting different values of y in the equation to get different values for x. Either way, we need points satisfying the equation to plot its graph
Related Questions to study
What is the relationship between the sign of the binomial and the sign of the second term in the product?
What is the relationship between the sign of the binomial and the sign of the second term in the product?
Find the product. (2𝑥 − 1)2
This question can be easily solved by using the formula
(a - b)2 = a2 - 2ab + b2
Find the product. (2𝑥 − 1)2
This question can be easily solved by using the formula
(a - b)2 = a2 - 2ab + b2
The coefficient of 𝑥 in the product (𝑥 − 3) (𝑥 − 5) is
The coefficient of 𝑥 in the product (𝑥 − 3) (𝑥 − 5) is
Find the product. (𝑥 + 9)(𝑥 + 9)
This question can be easily solved by using the formula
(a + b)2 = a2 + 2ab + b2
Find the product. (𝑥 + 9)(𝑥 + 9)
This question can be easily solved by using the formula
(a + b)2 = a2 + 2ab + b2
Geeta spends 803.94 to buy a necklace and bracelet set for each of her friends. Each
necklace costs Rs 7.99 and each bracelet cost 5.89, how many necklace and bracelet
What sets did she buy?
Geeta spends 803.94 to buy a necklace and bracelet set for each of her friends. Each
necklace costs Rs 7.99 and each bracelet cost 5.89, how many necklace and bracelet
What sets did she buy?
Use either the square of a binomial or difference of squares to find the area of the square.
![](data:image/png;base64,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)
Use either the square of a binomial or difference of squares to find the area of the square.
![](data:image/png;base64,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)
Use a table to find the product.
(2𝑥 + 1) (4𝑥 + 1)
Use a table to find the product.
(2𝑥 + 1) (4𝑥 + 1)
Graph the equation
on a coordinate plane.
Graph the equation
on a coordinate plane.
Use a table to find the product.
(𝑥 − 6) (3𝑥 + 4)
Use a table to find the product.
(𝑥 − 6) (3𝑥 + 4)
Why the product of two binomials (𝑎 + 𝑏) and (𝑎 − 𝑏) is a binomial instead of a trinomial?
Why the product of two binomials (𝑎 + 𝑏) and (𝑎 − 𝑏) is a binomial instead of a trinomial?
Graph the equation ![straight Y equals negative 0.5 straight x](data:image/png;base64,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)
We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. This makes plotting the graph simpler. We can also find the values by putting different values of y in the equation to get different values for x. Either way, we need points satisfying the equation to plot its graph.
Graph the equation ![straight Y equals negative 0.5 straight x](data:image/png;base64,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)
We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. This makes plotting the graph simpler. We can also find the values by putting different values of y in the equation to get different values for x. Either way, we need points satisfying the equation to plot its graph.
The constant term in the product (𝑥 + 3) (𝑥 + 4) is
The constant term in the product (𝑥 + 3) (𝑥 + 4) is
Write the product in standard form. (3𝑦 − 5)(3𝑦 + 5)
This question can be easily solved by using the formula
(a + b)(a - b) = a2 - b2
Write the product in standard form. (3𝑦 − 5)(3𝑦 + 5)
This question can be easily solved by using the formula
(a + b)(a - b) = a2 - b2
Write the product in standard form. (𝑥 − 4)(𝑥 + 4)
This question can be easily solved by using the formula
(a + b)(a - b) = a2 - b2
Write the product in standard form. (𝑥 − 4)(𝑥 + 4)
This question can be easily solved by using the formula
(a + b)(a - b) = a2 - b2