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An illustration shows a coordinate plane with four quadrants. The x and y axes extend from negative 10 to 10 in increments of 1. Two points are plotted on the graph. An upward slanting line connects the two points. Point A is plotted at coordinates left parenthesis 0 comma 6 right parenthesis. Point B is plotted at left parenthesis negative 2 comma 2 right parenthesis.

Identify the slope and y
-intercept of the line. Provide the most simplified form of the slope.

(1 point)
The slope is
. The y
-intercept is (0,
).
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1 answer

To determine the slope and y-intercept of the line connecting points A (0, 6) and B (-2, 2), we can follow these steps:

  1. Calculate the Slope (m): The slope of a line (m) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Let's assign the points:

    • Point A (x₁, y₁) = (0, 6)
    • Point B (x₂, y₂) = (-2, 2)

    Now substitute the coordinates into the slope formula: \[ m = \frac{2 - 6}{-2 - 0} = \frac{-4}{-2} = 2 \]

  2. Identify the Y-Intercept (b): The y-intercept of a line is the y-coordinate where the line crosses the y-axis. From Point A (0, 6), we see that the line crosses the y-axis at y = 6.

Thus, the outputs are as follows:

  • The slope is 2.
  • The y-intercept is (0, 6).

So, the final answer is: The slope is 2. The y-intercept is (0, 6).