The lines on the graph read through (o,5) (3,3) and (6,1) please answer the following

Question

What is the y-intercept
Wha is the slope
What is the equation of the line in slope-intercept form
This is a proportional or non proportional relationship

Answer 1

To analyze the relationship represented by the points (0, 5), (3, 3), and (6, 1), we can determine the y-intercept, slope, equation of the line in slope-intercept form, and whether it is proportional or non-proportional.

1. Y-intercept

The y-intercept is the value of \( y \) at \( x = 0 \). From the points provided, when \( x = 0 \), the value of \( y \) is \( 5 \).

Y-intercept: 5

2. Slope

The slope \( m \) can be calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

We can choose any two points, but let's use (0, 5) and (3, 3):

\[ m = \frac{3 - 5}{3 - 0} = \frac{-2}{3} = -\frac{2}{3} \]

Slope: -\(\frac{2}{3}\)

3. Equation of the line in slope-intercept form

The slope-intercept form of the equation of a line is given by:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept. Substituting the values we found:

\[ y = -\frac{2}{3}x + 5 \]

Equation of the line: \( y = -\frac{2}{3}x + 5 \)

4. Proportional or Non-Proportional Relationship

A proportional relationship means that the line passes through the origin (0,0). Since the y-intercept here is 5 (not 0), this indicates that the relationship is non-proportional.

Conclusion:

• Y-intercept: \( 5 \)
• Slope: \( -\frac{2}{3} \)
• Equation of the line: \( y = -\frac{2}{3}x + 5 \)
• The relationship is non-proportional.

Answer 2

For the Y intercept please say if it is one of these answers:
A: (0,0)
B: -5/3
C: y = 5x - 2
D: 7
E: (-5,0)
F: (0,5)
G: 0
H: y = 5x + 2/3

Answer 3

The y-intercept of the line, which is the point where the line crosses the y-axis, is (0, 5) based on the information provided.

From the options you've listed, the correct answer is:

F: (0, 5)

Answer 4

Ok thanks!

Answer 5

You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy learning!

Answer 6

which equation represents the graph described:
Dot 1: (0,3)
Dot 2: (2, -1)
Answers:
y=−4/5x+3
y is equal to negative 4 fifths x plus 3

y=3x+5
y is equal to 3 x plus 5

y=1/2x−1
y is equal to 1 half x minus 1

y=5/4x+3

Answer 7

To determine which equation represents the graph defined by the points (0, 3) and (2, -1), we first need to find the slope and then use the slope-intercept form to identify the correct equation.

1. Finding the slope

The slope \( m \) can be calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points \( (0, 3) \) and \( (2, -1) \):

• \( (x_1, y_1) = (0, 3) \)
• \( (x_2, y_2) = (2, -1) \)

Substituting these values into the slope formula:

\[ m = \frac{-1 - 3}{2 - 0} = \frac{-4}{2} = -2 \]

2. Using the slope to write the equation

Now that we have the slope \( m = -2 \) and we know the y-intercept is \( 3 \) (from the point (0, 3)), we can write the equation in slope-intercept form \( y = mx + b \):

\[ y = -2x + 3 \]

3. Checking the answer choices

Let's now check the given answer choices:

1. y = -4/5x + 3 (slope is -4/5)
2. y = 3x + 5 (slope is 3)
3. y = 1/2x - 1 (slope is 1/2)
4. y = 5/4x + 3 (slope is 5/4)

None of the provided equations match the equation we derived \( y = -2x + 3 \).

Therefore, based on the calculations, none of the given options correctly represent the equation for the line passing through the points (0, 3) and (2, -1). If the answer choices were intended to include this line, please double-check the options or the points provided.

Answer 8

Sorry I messed up on dot 2 its actually (1,-1)

Answer 9

No problem! Let's recalculate the slope and the equation using the correct points: (0, 3) and (1, -1).

1. Finding the slope

Using the points \( (0, 3) \) and \( (1, -1) \):

• \( (x_1, y_1) = (0, 3) \)
• \( (x_2, y_2) = (1, -1) \)

Now, we can calculate the slope \( m \):

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

2. Using the slope to write the equation

Now that we have the slope \( m = -4 \) and we know that the y-intercept is \( 3 \) (from the point (0, 3)), we can write the equation in slope-intercept form \( y = mx + b \):

\[ y = -4x + 3 \]

3. Checking the answer choices

Now let's check the provided answer choices against the equation we derived:

1. y = -4/5x + 3 (slope is -4/5)
2. y = 3x + 5 (slope is 3)
3. y = 1/2x - 1 (slope is 1/2)
4. y = 5/4x + 3 (slope is 5/4)

None of the given options match \( y = -4x + 3 \).

Conclusion

Again, it appears that none of the provided equations accurately represent the line defined by the points (0, 3) and (1, -1). Please feel free to provide more information or check for any possible error in the response options!

Answer 10

Could you try rearranging the problem such as (3,0) and (-1,1)

Answer 11

Sure! Let's find the equation of the line defined by the points (3, 0) and (-1, 1).

1. Finding the slope

Using the points \( (3, 0) \) and \( (-1, 1) \):

• \( (x_1, y_1) = (3, 0) \)
• \( (x_2, y_2) = (-1, 1) \)

The slope \( m \) is calculated as follows:

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

2. Using the slope to write the equation

Using the slope \( m = -\frac{1}{4} \) and the y-intercept, we can find the y-intercept by substituting one of the points into the slope-intercept form of the equation \( y = mx + b \).

Let's use the point \( (3, 0) \):

\[ 0 = -\frac{1}{4}(3) + b \] \[ 0 = -\frac{3}{4} + b \] \[ b = \frac{3}{4} \]

So the y-intercept is \( \frac{3}{4} \).

Putting this all together, the equation in slope-intercept form is:

\[ y = -\frac{1}{4}x + \frac{3}{4} \]

3. Checking with the answer choices

Now let's check this derived equation against the provided answer choices:

1. y = -4/5x + 3 (slope is -4/5)
2. y = 3x + 5 (slope is 3)
3. y = 1/2x - 1 (slope is 1/2)
4. y = 5/4x + 3 (slope is 5/4)

None of the given options match \( y = -\frac{1}{4}x + \frac{3}{4} \).

Conclusion

The equation representing the line going through the points (3, 0) and (-1, 1) is:

\[ y = -\frac{1}{4}x + \frac{3}{4} \]

However, it appears none of the provided options represent this equation. If you have other points or options, please share them!