A coordinate plane with a horizontal line passing through (negative 4, 4), (0, 4) and (4, 4). A coordinate plane with a line passing through (0, negative 3) and (3, 0).What is the equation in standard form of the line shown on the graph?x = 4y = 4x + y = 4x – y = 4

Answer 1

To determine the equation of the horizontal line that passes through the points (−4, 4), (0, 4), and (4, 4), we observe that all these points have the same y-coordinate of 4. Therefore, the equation of this horizontal line is:

\[ y = 4 \]

Now, let's consider the second line that passes through points (0, -3) and (3, 0). We can find the slope (m) of this line using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-3)}{3 - 0} = \frac{3}{3} = 1 \]

Next, we can use the point-slope form of the equation of a line, which is:

\[ y - y_1 = m(x - x_1) \]

Using the point (0, -3):

\[ y - (-3) = 1(x - 0) \] \[ y + 3 = x \] \[ y = x - 3 \]

To express this equation in standard form \(Ax + By = C\), we rearrange it:

\[ x - y = 3 \]

So, the standard form of the equation for the line passing through (0, -3) and (3, 0) is:

\[ x - y = 3 \]

To summarize, here are the equations of the lines:

1. Horizontal line: \(y = 4\)
2. Line through (0, -3) and (3, 0): \(x - y = 3\)

Answer 2

Julia wrote a linear equation in standard form as –6x – 3y = 10. Arthur noticed that the equation was not written in standard form and wants to tell Julia how to fix it. What advice should he give her?

Multiply both sides of the equation by –1, so that the value for A is positive.
Multiply both sides of the equation by 2, so that the values for A, B, and C have a greatest common factor other than 1.
Divide both sides of the equation by 3, so that the values for A, B, and C have a greatest common factor of 1.
Add 6x to both sides so that the value for A is 0.

Answer 3

In linear equations written in standard form, the general format is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) should ideally be non-negative.

Julia's equation is \(-6x - 3y = 10\). Here, the value for \(A\) (which is \(-6\)) is negative. To convert it into standard form, Arthur should advise Julia to multiply both sides of the equation by \(-1\) to make \(A\) positive.

Thus, the correct advice for Arthur to give Julia is:

Multiply both sides of the equation by –1, so that the value for A is positive.

This would change the equation to:

\[ 6x + 3y = -10 \]

Now, it is in standard form with a positive value for \(A\).

Answer 4

here the answer What is the equation in standard form of the line shown on the graph?

The equation of the line in standard form is

✔ 3
x +
✔ –4
y =
✔ 12
.

Austin determined that he has $13.50 in his piggy bank just in quarters and dimes. If q represents the number of quarters he has and d represents the number of dimes, which equation, written in standard form, represents this scenario?

q + d = 13.50
0.10q + 0.25d = 13.50
5q + 2d = 270
2q + 5d = 270

Answer 5

To find the correct equation representing the situation with Austin's quarters and dimes, we should consider the values of the coins and their quantities.

1. Quarters: Each quarter is worth $0.25.
2. Dimes: Each dime is worth $0.10.
3. Total Amount: Austin has $13.50.

We can express this using the number of quarters \(q\) and the number of dimes \(d\):

The equation that represents the total value of the coins in dollars can be formulated as: \[ 0.25q + 0.10d = 13.50 \]

To convert this equation to standard form (where integers are on one side), we can eliminate the decimals by multiplying the entire equation by 100:

\[ 100(0.25q) + 100(0.10d) = 100(13.50) \]

This results in: \[ 25q + 10d = 1350 \]

To further simplify, we can divide the entire equation by 5: \[ 5q + 2d = 270 \]

Thus, the equation that represents the scenario in standard form is: \[ \boxed{5q + 2d = 270} \]

So, the correct answer from the options listed is: 5q + 2d = 270.