What is the equation for the line in slope-intercept form?

Question

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Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 20 to 20 in increments of 2. The vertical y axis ranges from negative 20 to 20 in increments of 2. A line passes through points begin ordered pair negative 2 comma 13 end ordered pair and begin ordered pair 0 comma 5 end ordered pair and begin ordered pair 3 comma negative 7 end ordered pair and begin ordered pair 4 comma negative 11 end ordered pair.

Answer 1

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

1. Finding the slope (m): The slope formula is given by:

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

   We can choose two points from the graph. Let's use the points (0, 5) and (3, -7):

   \[ m = \frac{-7 - 5}{3 - 0} = \frac{-12}{3} = -4 \]

2. Finding the y-intercept (b): The y-intercept is the value of y when x = 0. From the point (0, 5), we can directly see that \( b = 5 \).

3. Writing the equation: Now that we have the slope \( m = -4 \) and the y-intercept \( b = 5 \), we can substitute these values into the slope-intercept form:

   \[ y = -4x + 5 \]

So, the equation for the line in slope-intercept form is:

\[ y = -4x + 5 \]