What is the slope of the linear function 10x+2y=6 ? Use any method of linear functions to solve.(1 point)

Question

m=

Answer 1

To find the slope of the linear function given by the equation \(10x + 2y = 6\), we can rearrange the equation into the slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope.

Starting with the equation:

\[ 10x + 2y = 6 \]

First, isolate \(y\) on one side of the equation. Subtract \(10x\) from both sides:

\[ 2y = -10x + 6 \]

Next, divide every term by \(2\) to solve for \(y\):

\[ y = -5x + 3 \]

Now, the equation is in the form \(y = mx + b\). From this, we can see that the slope \(m\) is:

\[ m = -5 \]

Thus, the slope of the linear function is:

\[ \boxed{-5} \]

Answer 2

Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?

Linear Function 1: y=15x+8
Linear Function 2:
x
y
5 26
13 34
(1 point)
Responses

Linear Function 1 has the greater rate of change, with a rate of change equal to 8 while Linear Function 2 has a rate of change equal to 1.
Linear Function 1 has the greater rate of change, with a rate of change equal to 8 while Linear Function 2 has a rate of change equal to 1.

Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 15.
Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 15.

Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 8.
Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 8.

Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.
Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.
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Answer 3

To compare the rates of change of Linear Function 1 and Linear Function 2, we can extract the slope (rate of change) from each.

Linear Function 1:
Given in slope-intercept form: \[ y = 15x + 8 \] The rate of change (slope) for Linear Function 1 is: \[ m_1 = 15 \]

Linear Function 2:
The data points provided are:

• When \(x = 5\), \(y = 26\)
• When \(x = 13\), \(y = 34\)

To find the slope (rate of change) for Linear Function 2, we use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points into the formula: \[ m_2 = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]

Now, we can compare the slopes:

• Rate of change for Linear Function 1: \(15\)
• Rate of change for Linear Function 2: \(1\)

Conclusion:
Linear Function 1 has the greater rate of change. The correct response is:

Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.

Answer 4

Compare Linear Function 1 with Linear Function 2. Which one has the lesser initial value?

Linear Function 1: Lionel’s cell phone plan costs $45 per month.
Linear Function 2: The relationship between the number of months Ruby has had her cell phone (x)
and the total cost (y)
is given by y=40x+60
.
(1 point)
Responses

Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $60.
Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $60.

Linear Function 1 has the lesser initial value, with an initial value equal to $45 while Linear Function 2 has an initial value equal to $60.
Linear Function 1 has the lesser initial value, with an initial value equal to $45 while Linear Function 2 has an initial value equal to $60.

Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $40.
Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $40.

Linear Function 2 has the lesser initial value, with an initial value equal to $40 while Linear Function 1 has an initial value equal to $45.
Linear Function 2 has the lesser initial value, with an initial value equal to $40 while Linear Function 1 has an initial value equal to $45.
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Answer 5

To compare the initial values of Linear Function 1 and Linear Function 2, we need to identify the initial values of both functions.

Linear Function 1:
Lionel’s cell phone plan costs $45 per month. This indicates that there is a fixed monthly cost of $45. However, the initial value when \(x = 0\) (when no months have passed) is typically represented as $0 if it only counts the monthly charges starting from 0. Therefore, we take the initial cost as:

• Initial value for Linear Function 1: $0

Linear Function 2:
The relationship is given by the equation: \[ y = 40x + 60 \] In this case, the initial value occurs when \(x = 0\): \[ y = 40(0) + 60 = 60 \] So, the initial value for Linear Function 2 is:

• Initial value for Linear Function 2: $60

Comparison of Initial Values:

• Linear Function 1: $0
• Linear Function 2: $60

Conclusion:
Linear Function 1 has the lesser initial value at $0, while Linear Function 2 has an initial value of $60.

The correct response is: Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $60.

Answer 6

Analyze the linear function whose slope is −3
and passes through the coordinate pair (−2,9)
. Which linear function matches this line?(1 point)
Responses

y=−3x+9
y equals negative 3 x plus 9

y=−2x−3
y equals negative 2 x minus 3

y=3x−3
y equals 3 x minus 3

y=−3x+3

Answer 7

To determine which linear function matches the line with a slope of \(-3\) that passes through the point \((-2, 9)\), we can use the point-slope form of the equation of a line, which is given by:

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

where \((x_1, y_1)\) is the point the line passes through and \(m\) is the slope.

In this case, \(m = -3\) and \((x_1, y_1) = (-2, 9)\).

Substituting these values into the formula, we have:

\[ y - 9 = -3(x - (-2)) \] \[ y - 9 = -3(x + 2) \]

Now, distribute \(-3\):

\[ y - 9 = -3x - 6 \]

Next, isolate \(y\) by adding \(9\) to both sides:

\[ y = -3x - 6 + 9 \] \[ y = -3x + 3 \]

Thus, the equation of the line is:

\[ y = -3x + 3 \]

Now we compare this with the provided options:

1. \(y = -3x + 9\)
2. \(y = -2x - 3\)
3. \(y = 3x - 3\)
4. \(y = -3x + 3\)

The correct function that matches our result is:

\(y = -3x + 3\)

Thus, the correct answer is: y = −3x + 3.

Answer 8

is 3x−4y=27 Linear or nonlinear?

Answer 9

The equation \(3x - 4y = 27\) is a linear equation.

To confirm that it is linear, we can rearrange the equation into the slope-intercept form, which is given by:

\[ y = mx + b \]

where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the original equation:

\[ 3x - 4y = 27 \]

We can isolate \(y\):

1. Subtract \(3x\) from both sides:

\[ -4y = -3x + 27 \]

2. Divide every term by \(-4\):

\[ y = \frac{3}{4}x - \frac{27}{4} \]

In this form, it is clear that the equation represents a straight line, indicating a linear relationship between \(x\) and \(y\).

Hence, the equation \(3x - 4y = 27\) is linear.

Answer 10

is 3x2−2x=4y Linear or nonlinear?

Answer 11

To determine whether the equation \(3x^2 - 2x = 4y\) is linear or nonlinear, we can analyze the terms in the equation.

1. Identify the Forms:

   • A linear equation in two variables (usually \(x\) and \(y\)) can be expressed in the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are constants, and the variables \(x\) and \(y\) are each raised only to the first power (i.e., they are not squared or raised to any other power).

2. Examine the Given Equation:

   • The given equation is \(3x^2 - 2x = 4y\).
   • Here, \(3x^2\) represents a term where \(x\) is squared, which means it is not a linear term.

Since the presence of the \(x^2\) term means that the relationship between \(x\) and \(y\) involves a variable raised to a power greater than 1, the equation is not linear.

Therefore, the equation \(3x^2 - 2x = 4y\) is nonlinear.