A functionf(x)

Question

is graphed on the coordinate plane.

What is the function rule in slope-intercept form?



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f(x)=


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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.

Answer 1

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: \[ f(x) = -4x - 2 \]