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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 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.

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

(1 point)
y
=
x+
Remaining Attempts : 3

1 answer

To find the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) using the two points given: (0, 2) and (1, -1).

  1. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]

  2. Use one of the points to find the y-intercept (b):
    We'll use the point (0, 2). Since this point is on the y-axis, the y-intercept is 2. \[ b = 2 \]

  3. Write the equation in slope-intercept form: Now that we know the slope is -3 and the y-intercept is 2, we can write the equation: \[ y = -3x + 2 \]

So, the equation of the line in slope-intercept form is: \[ y = -3x + 2 \]