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Question

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.

Write the equation of the line in slope-intercept form.

(1 point)
Responses

y=−5x−1
y equals negative 5 x minus 1

−5x−y=−1
negative 5 x minus y equals negative 1

y=−5x+1
y equals negative 5 x plus 1

y=5x+1
y equals 5 x plus 1
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Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b).

1. Find the slope (m): The slope can be calculated using two points on the line: (0, 1) and (1, -4).

   The formula for slope (m) is:

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

   Substituting the coordinates:

   • \( (x_1, y_1) = (0, 1) \)
   • \( (x_2, y_2) = (1, -4) \)

   \[ m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5 \]

2. Use the slope and a point to find the y-intercept (b): We can use the point (0, 1) to find the y-intercept. The y-intercept (b) is simply the value of y when x is 0.

   Since one of the points is (0, 1): \[ b = 1 \]

3. Write the equation: Now, we can plug the values of m and b into the slope-intercept form:

   \[ y = -5x + 1 \]

Thus, the correct response is:

y = -5x + 1