Which is the graph of 4x + 2y < 3?On a coordinate plane, a dashed straight line with negative slope goes through (0, 2) and (1, 0). Everything to the right of the line is shaded.On a coordinate plane, a dashed straight line with negative slope goes through (0, 2) and (1, 0). Everything to the left of the line is shaded.On a coordinate plane, a dashed straight line with positive slope goes through (negative 1, 0) and (0, 2). Everything to the left of the line is shaded.On a coordinate plane, a dashed straight line with positive slope goes through (negative 1, 0) and (0, 2). Everything to the right of the line is shaded.

Answer 1

To determine which graph corresponds to the inequality \(4x + 2y < 3\), we first need to rewrite the inequality in slope-intercept form (i.e., \(y = mx + b\)).

Starting with the inequality:

\[ 4x + 2y < 3 \]

Subtract \(4x\) from both sides:

\[ 2y < -4x + 3 \]

Now, divide by 2 to isolate \(y\):

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

This tells us the following:

1. The line \(y = -2x + \frac{3}{2}\) is the boundary line. Since the inequality is a strict inequality (<), the line will be dashed to indicate that points on the line are not included in the solution set.
2. The line has a negative slope of \(-2\) and a y-intercept of \(\frac{3}{2}\) (which is 1.5).
3. The area below the line represents the solutions to the inequality \(y < -2x + \frac{3}{2}\).

Next, we identify key points:

• When \(x = 0\), \(y = \frac{3}{2} = 1.5\) (the y-intercept).
• When \(x = 1\), substituting into the equation gives \(y = -2(1) + \frac{3}{2} = -2 + 1.5 = -0.5\) (a point below the intercept).

Now let’s check the options provided:

1. A dashed straight line with negative slope goes through \((0, 2)\) and \((1, 0)\) with shading to the right - this does not fit.
2. A dashed straight line with negative slope goes through \((0, 2)\) and \((1, 0)\) with shading to the left - this does not represent our line.
3. A dashed straight line with positive slope goes through \((-1, 0)\) and \((0, 2)\) with shading to the left - this does not fit since the slope is positive.
4. A dashed straight line with positive slope goes through \((-1, 0)\) and \((0, 2)\) with shading to the right - this also does not fit.

Based on this analysis, there's an inconsistency with the options provided against our derived line and shading.

Conclusion: The correct graph will show a dashed line with a negative slope through \((0, \frac{3}{2})\) and another point derived from the line, shading the area below this line (to the left of the line as it slopes downwards). Unfortunately, none of the options perfectly match this description. Please verify the possible options again.

Answer 2

Which is the graph of 4x + 2y < 3? graph 1 On a coordinate plane, a dashed straight line with negative slope goes through (0, 2) and (1, 0). Everything to the right of the line is shaded. graph 2 On a coordinate plane, a dashed straight line with negative slope goes through (0, 2) and (1, 0). Everything to the left of the line is shaded. graph 3 On a coordinate plane, a dashed straight line with positive slope goes through (negative 1, 0) and (0, 2). Everything to the left of the line is shaded. graph 4 On a coordinate plane, a dashed straight line with positive slope goes through (negative 1, 0) and (0, 2). Everything to the right of the line is shaded.

Answer 3

To analyze the inequality \(4x + 2y < 3\), we first rewrite it in slope-intercept form \(y < mx + b\).

Starting with the inequality:

\[ 4x + 2y < 3 \]

Subtracting \(4x\) from both sides gives us:

\[ 2y < -4x + 3 \]

Now, dividing everything by \(2\):

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

This indicates:

• The line \(y = -2x + \frac{3}{2}\) is the boundary line.
• It has a negative slope (\(-2\)) and a y-intercept of \(\frac{3}{2}\) (which is 1.5).
• Since the inequality is strict (<), the line will be dashed, indicating that points on the line are not included in the solution set.
• The area below the line (where \(y\) values are less than \(y = -2x + \frac{3}{2}\)) represents the solutions to the inequality.

Next, let's consider the points on the line:

• When \(x = 0\), \(y = \frac{3}{2} = 1.5\).
• When \(x = 1\), substituting into the equation gives \(y = -2(1) + \frac{3}{2} = -2 + 1.5 = -0.5\).

Now, let's look at the graph options:

1. Graph 1: A dashed straight line with negative slope going through (0, 2) and (1, 0) with shading to the right. This does not fit because the line's slope and shading do not match.
2. Graph 2: A dashed straight line with negative slope going through (0, 2) and (1, 0) with shading to the left. This does not match either as the correct line intercepts at (0, 1.5).
3. Graph 3: A dashed straight line with positive slope going through (-1, 0) and (0, 2) with shading to the left. This does not match as the slope is positive, which is not correct for our inequality.
4. Graph 4: A dashed straight line with positive slope going through (-1, 0) and (0, 2) with shading to the right. This also does not match as the slope is positive.

Since the correct graph should feature a downslope line with a negative slope (going down from left to right), and shading below this line, none of the provided options correctly represents the graph of \(4x + 2y < 3\).

Please double-check the graphs provided for any inconsistencies with the inequality we solved. The correct graph should have a dashed line with a negative slope that corresponds to intersecting the y-axis at \(y = 1.5\) and shading the area below that line.

Answer 4

its the line going upward left corner shaded left not right. aka graph 2

On a coordinate plane, a dashed straight line with negative slope goes through (0, 4) and (1.3, 0). Everything to the left of the line is shaded.Analyze the graph. Which inequality represents the graph?y > Negative one-thirdx + 4y < Negative one-thirdx + 4y > –3x + 4y < –3x + 4

Answer 5

Let's analyze the graph described: a dashed line with a negative slope that goes through points \((0, 4)\) and \((1.3, 0)\), with the area to the left of the line shaded.

1. Finding the equation of the line:

   We have two points: \((0, 4)\) and \((1.3, 0)\).

   The slope \(m\) of the line can be calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{1.3 - 0} = \frac{-4}{1.3} = -\frac{40}{13} \]

   Now we can use the point-slope form of a line, using the point \((0, 4)\): \[ y - 4 = -\frac{40}{13}(x - 0) \]

   This simplifies to: \[ y = -\frac{40}{13}x + 4 \]

2. Identifying the inequality:

   Since the line is dashed, it represents a strict inequality. The shaded region is to the left of the line, indicating that we are dealing with a "less than" inequality. Thus, we have: \[ y < -\frac{40}{13}x + 4 \]

3. Comparing with the given options: Let's rewrite the possible inequalities to see if they match our derived inequality:

   • Option 1: \(y > -\frac{1}{3}x + 4\)
   • Option 2: \(y < -\frac{1}{3}x + 4\)
   • Option 3: \(y > -3x + 4\)
   • Option 4: \(y < -3x + 4\)

   The slope of the derived inequality is \(-\frac{40}{13}\), which is approximately \(-3.08\). This is significantly steeper than \(-\frac{1}{3}\) and even slightly steeper than \(-3\), so we can eliminate \(y > -\frac{1}{3}x + 4\) and \(y > -3x + 4\).

   Since the analysis shows that the inequality is a "less than" condition (due to the direction of shading), we must select between:

   • Option 2: \(y < -\frac{1}{3}x + 4\)
   • Option 4: \(y < -3x + 4\)

   Given that \(-\frac{40}{13}\) is steeper than \(-3\), the correct inequality that matches the dashed line and the shading would be:

   The correct answer is Option 4: \(y < -3x + 4\).

The graph's left shading indicates values of \(y\) are less than those represented by the line, verifying the direction of the inequality.