Writing Linear Equations in Slope-Intercept Form Practice

Question

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Question
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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. A downward slanting line connects the two points. Point A is plotted at coordinates left parenthesis 0 comma negative 3 right parenthesis. Point B is plotted at left parenthesis negative 4 comma 0 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,
).

Answer 1

To find the slope and y-intercept of the line that connects the points A (0, -3) and B (-4, 0), we can follow these steps:

1. Calculate the slope (m): The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points A(0, -3) and B(-4, 0):

   • \( x_1 = 0, y_1 = -3 \)
   • \( x_2 = -4, y_2 = 0 \)

   Plugging in the values: \[ m = \frac{0 - (-3)}{-4 - 0} = \frac{3}{-4} = -\frac{3}{4} \]

2. Identify the y-intercept (b): The y-intercept is the point where the line crosses the y-axis. From point A, we see that when \( x = 0 \), \( y = -3 \), which means the y-intercept is \( (0, -3) \).

Therefore, we can summarize:

• The slope is \(-\frac{3}{4}\).
• The y-intercept is \( (0, -3) \).

Final answers:

• The slope is \(-\frac{3}{4}\). The y-intercept is \( (0, -3) \).