Which line represents the linear equation

Question

–3y = 15 – 4x?
A coordinate grid with 4 lines. Line A passes through (0, 5) and (4, 3.75). Line B passes through (3.75, 0) and (0, negative 5). Line C passes through (0, negative 5) and (negative 3.75, 0). Line D passes through (negative 3.75, 0) and (0, 5).
The equation –3y = 15 – 4x rewritten in slope-intercept form is
y
=
–(4/3)x
– 5
y
=
–(4/3)x
+ 5
y
= (4/3)x
– 5
y
= (4/3)x
+ 5.
choose one of them
The y-intercept is –5

–4/3
4/3
5 choose one of them and the slope of the line is –5

–4/3
4/3
5.
choose one of them
Line
A
B
C
D choose one of them is the graph of the line –3y = 15 – 4x.

Answer 1

Let's start by rewriting the given equation \(-3y = 15 - 4x\) in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

1. Rearranging the equation: \(-3y = 15 - 4x\)

   Divide each term by -3:

   \[ y = \frac{4}{3}x - 5 \]

Now we can extract the slope and y-intercept from the equation:

• The slope \(m\) is \(\frac{4}{3}\).
• The y-intercept \(b\) is \(-5\).

Select the options:

• The rewritten equation is:

  y = (4/3)x - 5 (correct choice)

• The y-intercept is:

  -5 (correct choice)

• The slope of the line is:

  4/3 (correct choice)

Identify the correct line:

Now we can identify which line from A, B, C, or D corresponds to this equation.

• Line A: Passes through (0, 5) and (4, 3.75). (y-intercept is 5, so it’s not correct)
• Line B: Passes through (3.75, 0) and (0, -5). (y-intercept is -5, could be correct)
• Line C: Passes through (0, -5) and (-3.75, 0). (y-intercept is -5, could be correct)
• Line D: Passes through (-3.75, 0) and (0, 5). (y-intercept is 5, so it’s not correct)

To find out whether line B or C is correct, we need to calculate the slope of both lines.

• Line B: Slope between (3.75, 0) and (0, -5): \(m = \frac{-5 - 0}{0 - 3.75} = \frac{-5}{-3.75} = \frac{5}{3}\) (not equal to \(\frac{4}{3}\), hence not correct)

• Line C: Slope between (0, -5) and (-3.75, 0): \(m = \frac{0 - (-5)}{-3.75 - 0} = \frac{5}{-3.75} = -\frac{4}{3}\) (matches the slope)

Conclusion:

Thus, Line C correctly represents the linear equation \(-3y = 15 - 4x\).

Final selections:

1. Rewritten equation: y = (4/3)x - 5
2. Y-intercept: -5
3. Slope: 4/3
4. Correct line: C

Answer 2

not line C try again

Answer 3

Let’s double-check the equation and the line interpretations step by step.

We started with the equation:

\[ -3y = 15 - 4x \]

Converting to Slope-Intercept Form

Dividing everything by -3 gives us:

\[ y = \frac{4}{3}x - 5 \]

From this equation:

• The y-intercept (b) is \(-5\).
• The slope (m) is \(\frac{4}{3}\).

Analyzing the Lines:

1. Line A passes through (0, 5) and (4, 3.75):

   • Y-intercept is 5, so this line does not match.

2. Line B passes through (3.75, 0) and (0, -5):

   • Y-intercept is -5, which matches.
   • Calculating the slope: \[ m = \frac{0 - (-5)}{3.75 - 0} = \frac{5}{3.75} = \frac{5}{3.75} = \frac{4}{3} \]
   • This matches both the y-intercept and the slope.

3. Line C passes through (0, -5) and (-3.75, 0):

   • Y-intercept is -5, which matches.
   • Calculating the slope: \[ m = \frac{0 - (-5)}{-3.75 - 0} = \frac{5}{-3.75} = -\frac{4}{3} \]
   • The slope does not match; it’s negative.

4. Line D passes through (-3.75, 0) and (0, 5):

   • Y-intercept is 5, so this line does not match.

Conclusion

The correct line is:

• Line B: It has the correct y-intercept (-5) and slope (\(\frac{4}{3}\)).

Final Selections:

1. Rewritten equation: y = (4/3)x - 5
2. Y-intercept: -5
3. Slope: \(\frac{4}{3}\)
4. Correct line: B

I apologize for the confusion earlier! Thank you for your patience.

Answer 4

Consider this system of linear equations:

y = –3x + 5

y = mx + b

Which values of m and b will create a system of linear equations with no solution?

m = –3 and b = –3
m = 5 and b = –3
m = 3 and b = 5
m = -3 and b = 5

Answer 5

A system of linear equations will have no solution when the lines represented by the equations are parallel. This occurs when the slopes of the lines are equal, but the y-intercepts are different.

Let's analyze the given equations:

1. The first equation is: \[ y = -3x + 5 \] Here, the slope \(m_1\) is \(-3\) and the y-intercept \(b_1\) is \(5\).

2. The second equation is: \[ y = mx + b \] For this equation, the slope \(m_2\) is \(m\), and the y-intercept \(b_2\) is \(b\).

To create a system with no solution:

• The slopes must be equal: \[ m = -3 \]
• The y-intercepts must be different: \[ b \neq 5 \]

Analyzing the choices:

1. m = -3 and b = -3:

   • Slopes are equal. (m = -3)
   • Y-intercepts are different. (b = -3 is different from 5)
   • This choice has no solution.

2. m = 5 and b = -3:

   • Slopes are not equal (m = 5, \(m_1 = -3\)).
   • This choice has a solution.

3. m = 3 and b = 5:

   • Slopes are not equal (m = 3, \(m_1 = -3\)).
   • This choice has a solution.

4. m = -3 and b = 5:

   • Slopes are equal (m = -3).
   • Y-intercepts are the same (b = 5).
   • This choice represents the same line (infinite solutions).

Conclusion:

The only values of \(m\) and \(b\) that will create a system of linear equations with no solution are:

• m = -3 and b = -3.

Answer 6

Abed says he has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is y = 3x – 1. Which could be the other equation?

y = 3x + 2
3x – y = 2
3x – y = 1
3x + y = 1

Answer 7

In order for a system of linear equations to have an infinite number of solutions, the equations must represent the same line. This means they need to have the same slope and y-intercept.

Given one of the equations is:

\[ y = 3x - 1 \]

The slope \(m\) of this equation is \(3\), and the y-intercept \(b\) is \(-1\).

Now let's analyze each option:

1. y = 3x + 2

   • Slope: \(3\)
   • Y-intercept: \(2\)
   • Different y-intercept from the first equation, so not equivalent.

2. 3x – y = 2

   • Rearranging this to slope-intercept form: \[ -y = -3x + 2 \quad \Rightarrow \quad y = 3x - 2 \]
   • Slope: \(3\)
   • Y-intercept: \(-2\)
   • Different y-intercept from the first equation, so not equivalent.

3. 3x – y = 1

   • Rearranging this to slope-intercept form: \[ -y = -3x + 1 \quad \Rightarrow \quad y = 3x - 1 \]
   • Slope: \(3\)
   • Y-intercept: \(-1\)
   • Same equation as the first one. This equation is equivalent (same line), so this option works.

4. 3x + y = 1

   • Rearranging this to slope-intercept form: \[ y = -3x + 1 \]
   • Slope: \(-3\)
   • Y-intercept: \(1\)
   • Different slope from the first equation, so not equivalent.

Conclusion:

The other equation that could create a system with an infinite number of solutions, being equivalent to \(y = 3x - 1\), is:

3x – y = 1.

Answer 8

Solve the system of linear equations by graphing.

y = –y equals negative StartFraction 5 over 2 EndFraction minus 7.x – 7

x + 2y = 4

What is the solution to the system of linear equations?

(–4.5, 4.25)
(–1.7, –2.8)
(0, –7)
(3, 0.5)

Answer 9

To solve the system of equations by graphing, first we need to convert both equations into slope-intercept form (y = mx + b) if necessary.

Given equations:

1. Equation 1: \[ y = -\frac{5}{2}x - 7 \] This equation is already in slope-intercept form, where the slope \(m = -\frac{5}{2}\) and the y-intercept \(b = -7\).

2. Equation 2: \[ x + 2y = 4 \] Rearranging to slope-intercept form: \[ 2y = -x + 4 \] \[ y = -\frac{1}{2}x + 2 \] Here, the slope \(m = -\frac{1}{2}\) and the y-intercept \(b = 2\).

Now, let's determine the intersections of the two lines.

Graph and Find the Intersection Points:

1. Graph of the first equation \(y = -\frac{5}{2}x - 7\):

   • When \(x = 0\), \(y = -7\) (point \( (0, -7) \))
   • When \(x = 2\), \(y = -\frac{5}{2}(2) - 7 = -5 - 7 = -12\) (point \( (2, -12) \))

2. Graph of the second equation \(y = -\frac{1}{2}x + 2\):

   • When \(x = 0\), \(y = 2\) (point \( (0, 2) \))
   • When \(x = 4\), \(y = -\frac{1}{2}(4) + 2 = -2 + 2 = 0\) (point \( (4, 0) \))

Finding the Solution:

To find the solution to the system of equations, we should look for the point that satisfies both equations (the intersection of the two lines).

Using the equations, we could also find the intersection algebraically:

Setting the two equations equal: \[ -\frac{5}{2}x - 7 = -\frac{1}{2}x + 2 \] To eliminate the fractions, multiply through by \(2\): \[ -5x - 14 = -x + 4 \] Adding \(5x\) and \(x\) gives: \[ -14 = 4 + 6x \] Subtract \(4\) from both sides: \[ -18 = 6x \] Now divide by \(6\): \[ x = -3 \]

Substituting \(x = -3\) back into one of the equations to solve for \(y\): \[ y = -\frac{5}{2}(-3) - 7 = \frac{15}{2} - 7 = \frac{15}{2} - \frac{14}{2} = \frac{1}{2} \]

Thus, the solution to the system of equations is \((-3, 0.5)\).

Check the Options:

The given options are:

1. (–4.5, 4.25)
2. (–1.7, –2.8)
3. (0, –7)
4. (3, 0.5)

None of these options match the calculated intersection of \((-3, 0.5)\). I recommend double-checking the options provided; it seems there has been a mistake or disconnect between the results and the multiple-choice options.

Answer 10

well your answer is bad its one of the options and its not (3, 0.5) or the negative version

Answer 11

Let's revisit the problem step-by-step and solve it accurately to identify the correct solution from the provided options.

Given Equations:

1. Equation 1: \( y = -\frac{5}{2}x - 7 \)

2. Equation 2: \( x + 2y = 4 \)

Convert Equation 2 to Slope-Intercept Form:

To convert \( x + 2y = 4 \) to slope-intercept form (y = mx + b):

1. Isolate \( 2y \): \[ 2y = -x + 4 \]

2. Divide by 2: \[ y = -\frac{1}{2}x + 2 \]

Now we have the two equations:

1. \( y = -\frac{5}{2}x - 7 \) (Equation 1)
2. \( y = -\frac{1}{2}x + 2 \) (Equation 2)

Finding the Intersection Point:

To find the solution to the system of equations, we set the two equations equal to each other:

\[ -\frac{5}{2}x - 7 = -\frac{1}{2}x + 2 \]

Solve for \(x\):

1. First, eliminate the fractions by multiplying the entire equation by \(2\): \[ -5x - 14 = -x + 4 \]

2. Rearranging gives: \[ -5x + x = 4 + 14 \] \[ -4x = 18 \] \[ x = -\frac{18}{4} = -\frac{9}{2} = -4.5 \]

Substitute \(x\) Back to Find \(y\):

Using \(y = -\frac{5}{2}(-4.5) - 7\): \[ y = -\frac{5}{2} \cdot (-4.5) - 7 \] Calculating the first part: \[ y = \frac{5 \cdot 4.5}{2} - 7 \] \[ = \frac{22.5}{2} - 7 \] \[ = 11.25 - 7 \] \[ = 4.25 \]

Conclusion:

The solution to the system of linear equations is: \[ (-4.5, 4.25) \]

Thus, the correct matching answer from the provided options is:

(–4.5, 4.25).

Thank you for your patience, and I apologize for any confusion in the earlier responses!