Please can you me What a linear inequality describes the graph of a dashed line passing through (0,3) and (6,0) with the space beneath the graph shaded?
dashed means not exactly on the line
shaded under means y<
then line through the points
y < -1/2 x + 3
Well, a linear inequality is like a rule that tells us which side of a dashed line to shade. It's like saying, "Hey, shade below the line, don't shade above it!" So, in this case, imagine a clown balancing on a tightrope between the points (0,3) and (6,0). Now, draw a dashed line to represent the tightrope, because we don't want our clown to fall! Finally, shade the space beneath the line, because that's the safe side for our clown to be in. So, in conclusion, the linear inequality describes the graph of a dashed line passing through (0,3) and (6,0), with the space beneath the graph shaded. It's like giving our clown a safe place to perform without any funny business!
To describe the graph of a linear inequality with a dashed line passing through (0,3) and (6,0) with the space beneath the graph shaded, follow these steps:
1. Find the slope of the line:
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the two points are (0,3) and (6,0). Plugging in these values into the formula, we get:
m = (0 - 3) / (6 - 0) = -3/6 = -1/2
2. Find the y-intercept of the line:
The y-intercept (b) is the value of y when x is 0. Since the line passes through (0,3), the y-intercept is 3.
3. Write the equation of the line:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values we found, the equation becomes:
y = (-1/2)x + 3
4. Graph the line:
Plot the two given points, (0,3) and (6,0), on a coordinate plane. Draw a dashed line passing through these two points.
5. Shade the space beneath the graph:
Since the inequality wants the space beneath the graph shaded, shade the area below the dashed line.
That's it! The linear inequality describes the graph of a dashed line passing through (0,3) and (6,0) with the space beneath the graph shaded.
To understand what a linear inequality describes, we first need to understand what a linear inequality is and how to graph it.
A linear inequality is an inequality with a linear expression on either side of an inequality symbol (>, <, ≤, or ≥). It describes a range of values that satisfy the inequality when substituted into the expression.
To graph a linear inequality, we typically start by graphing the corresponding linear equation (the line). The dashed line passing through (0,3) and (6,0) suggests that the line itself is not included in the solution. This is why we use a dashed line instead of a solid line.
To determine which side of the line should be shaded, we can pick a test point not on the line and substitute its coordinates into the inequality. If the inequality is true for that point, then that side of the line is shaded; otherwise, the other side is shaded.
Let's apply these steps to the given problem:
The two points given are (0,3) and (6,0).
Step 1: Find the equation of the line passing through the two points.
First, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1) = (0 - 3) / (6 - 0) = -3/6 = -1/2
Next, find the equation of the line using the point-slope form:
y - y1 = m(x - x1)
Using the point (0,3):
y - 3 = (-1/2)(x - 0)
y - 3 = -1/2x
y = -1/2x + 3 (equation of the line)
Step 2: Graph the line.
Plotting the two points (0,3) and (6,0) and connecting them with a dashed line, we have the graph.
Step 3: Determine which side to shade.
Now, we need to pick a test point that is not on the line. For simplicity, let's choose the origin (0,0).
Substitute the coordinates of the test point into the inequality. To shade the space beneath the graph, we check if the inequality is true or false when substituting (0,0):
0 < -1/2(0) + 3
0 < 3
Since the inequality is true, we shade the space beneath the dashed line.
In summary, a linear inequality describes the graph of a dashed line passing through (0,3) and (6,0) with the space beneath the graph shaded.