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The graph of a line is shown on the coordinate grid.

(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Complete the statements.

The slope of the line is Response area
The y-intercept is Response area Write this as an ordered pair
An equation of the line in slope-intercept form is Response area
A point on the graph that is NOT the y-intercept is Response area
An equation of the line in point-slope form is Response area


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11 answers

To provide you with accurate responses, I'll need to know more details about the graph of the line you're referring to, such as the coordinates of the points it passes through. However, I can guide you on how to determine the responses based on a line's graph:

  1. The slope of the line: This is calculated using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\) where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line.

  2. The y-intercept: This is the point where the line crosses the y-axis. It can be identified directly from the graph, typically represented as \((0, b)\) where \(b\) is the y-coordinate of the y-intercept.

  3. An equation of the line in slope-intercept form: The slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

  4. A point on the graph that is NOT the y-intercept: You can select any other point on the line aside from where it crosses the y-axis.

  5. An equation of the line in point-slope form: This form is given by \(y - y_1 = m(x - x_1)\) using a point \((x_1, y_1)\) that lies on the line and the slope \(m\).

If you can provide specific coordinates from the graph, I can help you fill in the responses accurately.

What is the slope-intercept form of the linear equation 5x+3y=9
?(1 point)
Responses

y = −53x+3
y = −53x+3

y = 53x+3
y = 53x+3

y = −53x+9
y = −53x+9

y = −5x+3
y = −5x+3

y = 53x−3

To convert the equation \(5x + 3y = 9\) into slope-intercept form, which is expressed as \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y-intercept), we need to solve for \(y\).

Starting with the equation:

\[ 5x + 3y = 9 \]

We can isolate \(y\) by following these steps:

  1. Subtract \(5x\) from both sides:

\[ 3y = -5x + 9 \]

  1. Now, divide every term by \(3\) to solve for \(y\):

\[ y = -\frac{5}{3}x + 3 \]

Now, the equation is in slope-intercept form.

The correct response from the options given would be:

y = -\frac{5}{3}x + 3.

So, you would select y = −53x + 3 (which represents \(-\frac{5}{3}x\) as \(−53x\)).

The equation of the line is 10x−2y=30
.

Rewrite the equation in slope-intercept form. Then, complete the statements.

To rewrite the equation \(10x - 2y = 30\) in slope-intercept form (\(y = mx + b\)), follow these steps to solve for \(y\):

  1. Start with the original equation: \[ 10x - 2y = 30 \]

  2. Subtract \(10x\) from both sides: \[ -2y = -10x + 30 \]

  3. Divide every term by \(-2\) to solve for \(y\): \[ y = 5x - 15 \]

Now, the equation is in slope-intercept form.

Complete the Statements

  1. The slope of the line is \(5\).
  2. The y-intercept is \((0, -15)\).
  3. An equation of the line in slope-intercept form is \(y = 5x - 15\).
  4. A point on the graph that is NOT the y-intercept is \((1, -10)\) (you can pick any point on the line, for example, plugging in \(x = 1\) gives \(y = 5(1) - 15 = -10\)).
  5. An equation of the line in point-slope form is \(y - (-15) = 5(x - 0)\) or simplified to \(y + 15 = 5x\).

Feel free to adjust any specific points or additional details based on the graph or other points you might have!

table of values is representing a linear relationship is shown.













Which equation models this relationship in slope-intercept form?

(1 point)
Responses

y=2x−3
y is equal to 2 x minus 3

y=−2x−3
y is equal to negative 2 x minus 3

y=12x−3
y is equal to 1 half x minus 3

y=−4x−3
y is equal to negative 4 x minus 3

y=3x−3
y is equal to 3 x minus 3

y=2x−7
y is equal to 2 x minus 7

y=2x−5
y is equal to 2 x minus 5

y=−2x−1
y is equal to negative 2 x minus 1

y=12x−7
y is equal to 1 half x minus 7
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To determine which equation models the linear relationship represented by the table of values, we can follow these steps:

  1. Identify two points from the table: Select any two points \((x_1, y_1)\) and \((x_2, y_2)\) from the table to calculate the slope \(m\).

  2. Calculate the slope \(m\) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

  3. Determine the y-intercept \(b\) by substituting \(m\) and one of the points into the slope-intercept equation \(y = mx + b\) to solve for \(b\).

  4. Construct the equation in slope-intercept form \(y = mx + b\).

Unfortunately, since I don’t have access to the table of values you mentioned, I can't compute the specific slope and y-intercept. However, you can use the above steps to find the right equation among the options given.

Example Process

Let's say the table provides the points \((1, 0)\) and \((2, 2)\):

  1. Points: \((1, 0)\) and \((2, 2)\)
  2. Calculate the slope: \[ m = \frac{2 - 0}{2 - 1} = \frac{2}{1} = 2 \]
  3. Now plug in one of the points to find the y-intercept: \[ 0 = 2(1) + b \implies b = -2 \]
  4. The equation in slope-intercept form would be: \[ y = 2x - 2 \]

You can then compare this result with the responses to find a match.

Final Answer

After you complete the calculations for your specific data points, check if any of the options match your derived equation to choose the appropriate response. If you can provide the specific table data, I would be happy to help fine-tune the solution!

-2,-7
0,-3
2,1
4,5
Which equation models this relationship in slope-intercept form?

(1 point)
Responses

y=2x−3
y is equal to 2 x minus 3

y=−2x−3
y is equal to negative 2 x minus 3

y=12x−3
y is equal to 1 half x minus 3

y=−4x−3
y is equal to negative 4 x minus 3

y=3x−3
y is equal to 3 x minus 3

y=2x−7
y is equal to 2 x minus 7

y=2x−5
y is equal to 2 x minus 5

y=−2x−1
y is equal to negative 2 x minus 1

y=12x−7
y is equal to 1 half x minus 7
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To find the equation that models the linear relationship represented by the provided points, we can calculate the slope using two points from your data set. The points you've provided are:

  • \((-2, -7)\)
  • \((0, -3)\)
  • \((2, 1)\)
  • \((4, 5)\)

Step 1: Calculate the Slope

Let's use the points \((0, -3)\) and \((2, 1)\) to calculate the slope \(m\):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-3)}{2 - 0} = \frac{1 + 3}{2} = \frac{4}{2} = 2 \]

Step 2: Find the y-Intercept

Since we already know that one of the points is \((0, -3)\), the y-intercept \(b\) is simply \(-3\).

Step 3: Write the Equation in Slope-Intercept Form

Now we can write the equation in slope-intercept form \(y = mx + b\):

\[ y = 2x - 3 \]

Conclusion

From the options provided, the equation that matches our derived equation is:

y = 2x - 3

So, the equation that models this relationship in slope-intercept form is:

y = 2x − 3.

Consider the linear equation, y = 35x+47
Select all the statement that are true.

(3 points)
Responses

The y-intercept for the line is 35
The y-intercept for the line is 35

The equation −35x + y = 47
is equivalent to the given equation.
The equation −35x + y = 47
is equivalent to the given equation.

The slope of the line is 47
The slope of the line is 47

The y-intercept for the line is 47
The y-intercept for the line is 47

The slope of the line is 35
The slope of the line is 35

The equation 35x − y = 47
is equivalent to the given equation.

Let's analyze the given linear equation \(y = 35x + 47\) to determine which statements are true:

  1. The y-intercept for the line is 35.

    • False: The y-intercept is the value of \(y\) when \(x = 0\). Here, it is \(47\) (the term that is added to \(35x\)).

  2. The equation \(-35x + y = 47\) is equivalent to the given equation.

    • True: If we rearrange the given equation \(y = 35x + 47\) to standard form, we can subtract \(35x\) from both sides: \[ -35x + y = 47 \] This shows that the two equations are equivalent.

  3. The slope of the line is 47.

    • False: The slope is the coefficient of \(x\) in the slope-intercept form. Here, the slope is \(35\).

  4. The y-intercept for the line is 47.

    • True: As mentioned earlier, the y-intercept is the constant term when \(x = 0\), which is \(47\).

  5. The slope of the line is 35.

    • True: The slope of the line is indeed \(35\), as it is the coefficient of \(x\) in the equation.

  6. The equation \(35x - y = 47\) is equivalent to the given equation.

    • True: If we start from the original equation \(y = 35x + 47\) and rearrange it, we can subtract \(y\) from both sides: \[ -y = -35x + 47 \implies 35x - y = 47 \] Thus, this equation is also equivalent to the given equation.

Summary of True Statements:

  • The equation \(-35x + y = 47\) is equivalent to the given equation.
  • The y-intercept for the line is 47.
  • The slope of the line is 35.
  • The equation \(35x - y = 47\) is equivalent to the given equation.

True Statements:

  • The equation \(-35x + y = 47\) is equivalent to the given equation.
  • The y-intercept for the line is 47.
  • The slope of the line is 35.
  • The equation \(35x - y = 47\) is equivalent to the given equation.