Slope and y-intercepts Practice

Question

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5 of 55 of 5 Items

Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. A downward slanting line is plotted on the coordinate plane. The downward slanting line with arrows on both ends passes through the following closed points: left parenthesis negative 3 comma 2.5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.

Determine the initial value and the rate of change of the linear function as given in the graph.

(1 point)
The initial value is
, and the rate of change is

Answer 1

Based on the points mentioned from the graph, we can determine the initial value (y-intercept) and the rate of change (slope) of the linear function.

Initial Value (y-intercept): The y-intercept is the point where the line crosses the y-axis. In the provided points, the line passes through the point (0, 1). Thus, the initial value is 1.

Rate of Change (Slope): The slope (rate of change) can be calculated using any two points on the line. Let's use the points (0, 1) and (2, 0).

The slope \( m \) is calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using (0, 1) as \((x_1, y_1)\) and (2, 0) as \((x_2, y_2)\):

\[ m = \frac{0 - 1}{2 - 0} = \frac{-1}{2} = -\frac{1}{2} \]

Therefore, the initial value is 1, and the rate of change is -1/2.