Question
2. A function is shown.
7x + 4y = 14
Which graph represents the function?
A
V
y
61
67
4 (0, 3.5)
4 (0, 3.5)
2+
(2, 0)
(-2, 0)
-4 -2 0 2.4
-4-2 0- 2 4
-2-
-2+
B
y
6+
61
+
4-
44
1(0, 2)
2
2
(3.5, 0)
(-3.5, 0)
+(0,2)
+x
-4 -2 - 2 4
4 -2 0 2 14
-2+
27. The graph of a line is shown.
y
6+
4
2+
-6
-4 -2 0 2 4 6
x
-21
-4.
-6+
Which equation represents the line?
1 y= x-0
m/in
13
y =
3
5
13
y =
=
-x
5
5
13
Y
x
3
3
16. Which function has the greatest slope?
5
(A)
Y
== x+1
3
V =
-x+ 8
3
5
Y
=
-X
-
4
4
3
V =
x+3
2
7x + 4y = 14
Which graph represents the function?
A
V
y
61
67
4 (0, 3.5)
4 (0, 3.5)
2+
(2, 0)
(-2, 0)
-4 -2 0 2.4
-4-2 0- 2 4
-2-
-2+
B
y
6+
61
+
4-
44
1(0, 2)
2
2
(3.5, 0)
(-3.5, 0)
+(0,2)
+x
-4 -2 - 2 4
4 -2 0 2 14
-2+
27. The graph of a line is shown.
y
6+
4
2+
-6
-4 -2 0 2 4 6
x
-21
-4.
-6+
Which equation represents the line?
1 y= x-0
m/in
13
y =
3
5
13
y =
=
-x
5
5
13
Y
x
3
3
16. Which function has the greatest slope?
5
(A)
Y
== x+1
3
V =
-x+ 8
3
5
Y
=
-X
-
4
4
3
V =
x+3
2
Answers
GPT-4o mini
Let's break down each part of your question:
### Part 1: Which graph represents the function \(7x + 4y = 14\)?
First, we can rewrite the equation in slope-intercept form \(y = mx + b\) to determine its characteristics.
1. Start with the equation:
\[
7x + 4y = 14
\]
2. Solve for \(y\):
\[
4y = -7x + 14
\]
\[
y = -\frac{7}{4}x + \frac{14}{4}
\]
\[
y = -\frac{7}{4}x + \frac{7}{2}
\]
From this, we can see:
- The y-intercept \(b = \frac{7}{2} = 3.5\) (point (0, 3.5))
- The slope \(m = -\frac{7}{4}\) (which indicates the line will slope downwards).
When choosing among the graphs, look for one that has:
- A point at (0, 3.5).
- A negative slope.
### Part 2: Which equation represents the line seen on the graph?
To find the correct equation for the line:
1. Identify any points on the graphed line.
2. Identify the slope from the graph (rise/run).
Assuming the coordinates shown in the question are points on the line, use the coordinates to compute the slope, and cover possible equations given to identify which matches;
### Part 3: Which function has the greatest slope?
Now, let's analyze the slopes of the provided functions:
- **(A)** \(y = x + 1\) - slope = 1
- **(B)** \(y = -x + 8\) - slope = -1
- **(C)** \(y = -\frac{1}{4}x + 3\) - slope = -0.25
- **(D)** \(y = \frac{1}{2}x + 4\) - slope = 0.5
From the above:
- The highest slope value is **1** from function (A) \(y = x + 1\).
### Summary
- Find the correct graph for \(7x + 4y = 14\), which should intersect the y-axis at (0, 3.5) and have a negative slope.
- Determine which line corresponds to the graphical features you've seen, possibly using point coordinates for verification.
- Choose **(A)** \(y = x + 1\) as the function with the greatest slope.
### Part 1: Which graph represents the function \(7x + 4y = 14\)?
First, we can rewrite the equation in slope-intercept form \(y = mx + b\) to determine its characteristics.
1. Start with the equation:
\[
7x + 4y = 14
\]
2. Solve for \(y\):
\[
4y = -7x + 14
\]
\[
y = -\frac{7}{4}x + \frac{14}{4}
\]
\[
y = -\frac{7}{4}x + \frac{7}{2}
\]
From this, we can see:
- The y-intercept \(b = \frac{7}{2} = 3.5\) (point (0, 3.5))
- The slope \(m = -\frac{7}{4}\) (which indicates the line will slope downwards).
When choosing among the graphs, look for one that has:
- A point at (0, 3.5).
- A negative slope.
### Part 2: Which equation represents the line seen on the graph?
To find the correct equation for the line:
1. Identify any points on the graphed line.
2. Identify the slope from the graph (rise/run).
Assuming the coordinates shown in the question are points on the line, use the coordinates to compute the slope, and cover possible equations given to identify which matches;
### Part 3: Which function has the greatest slope?
Now, let's analyze the slopes of the provided functions:
- **(A)** \(y = x + 1\) - slope = 1
- **(B)** \(y = -x + 8\) - slope = -1
- **(C)** \(y = -\frac{1}{4}x + 3\) - slope = -0.25
- **(D)** \(y = \frac{1}{2}x + 4\) - slope = 0.5
From the above:
- The highest slope value is **1** from function (A) \(y = x + 1\).
### Summary
- Find the correct graph for \(7x + 4y = 14\), which should intersect the y-axis at (0, 3.5) and have a negative slope.
- Determine which line corresponds to the graphical features you've seen, possibly using point coordinates for verification.
- Choose **(A)** \(y = x + 1\) as the function with the greatest slope.