Question
A functionf(x)
is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=
$\text{Basic}$
$x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$
$x\frac{ }{ }$
$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through the points begin ordered pair negative 0.5 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair and begin ordered pair negative 1 comma 2 end ordered pair.
is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=
$\text{Basic}$
$x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$
$x\frac{ }{ }$
$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through the points begin ordered pair negative 0.5 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair and begin ordered pair negative 1 comma 2 end ordered pair.
Answers
GPT-4o mini
To find the function rule in slope-intercept form \( f(x) = mx + b \), we first need to determine the slope \( m \) and the y-intercept \( b \) of the line.
1. **Finding the slope (m):**
The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can use any two points from the graph. Let's use the points \((-0.5, 0)\) and \((0, -2)\).
\( (x_1, y_1) = (-0.5, 0) \)
\( (x_2, y_2) = (0, -2) \)
Plugging in the values:
\[
m = \frac{-2 - 0}{0 - (-0.5)} = \frac{-2}{0.5} = -4
\]
2. **Finding the y-intercept (b):**
The y-intercept is the point at which the line crosses the y-axis. This occurs when \( x = 0 \). From the point \((0, -2)\), we see that when \( x = 0 \), \( y = -2 \). Therefore, the y-intercept \( b = -2 \).
3. **Putting it all together:**
Now that we have the slope \( m = -4 \) and the y-intercept \( b = -2 \), we can write the equation of the line in slope-intercept form:
\[
f(x) = -4x - 2
\]
Thus, the function rule in slope-intercept form is:
\[
f(x) = -4x - 2
\]
1. **Finding the slope (m):**
The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can use any two points from the graph. Let's use the points \((-0.5, 0)\) and \((0, -2)\).
\( (x_1, y_1) = (-0.5, 0) \)
\( (x_2, y_2) = (0, -2) \)
Plugging in the values:
\[
m = \frac{-2 - 0}{0 - (-0.5)} = \frac{-2}{0.5} = -4
\]
2. **Finding the y-intercept (b):**
The y-intercept is the point at which the line crosses the y-axis. This occurs when \( x = 0 \). From the point \((0, -2)\), we see that when \( x = 0 \), \( y = -2 \). Therefore, the y-intercept \( b = -2 \).
3. **Putting it all together:**
Now that we have the slope \( m = -4 \) and the y-intercept \( b = -2 \), we can write the equation of the line in slope-intercept form:
\[
f(x) = -4x - 2
\]
Thus, the function rule in slope-intercept form is:
\[
f(x) = -4x - 2
\]