It looks like you are trying to find the equation of a line given a set of points where \( x \) values are -1 and 2, and the corresponding \( y \) values are 10 and 2,160. To derive the equation of a line in the form \( y = mx + b \) (where \( m \) is the slope and \( b \) is the y-intercept), you can follow these steps:
-
Find the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, we'll use \( (x_1, y_1) = (-1, 10) \) and \( (x_2, y_2) = (2, 2160) \).
\[ m = \frac{2160 - 10}{2 - (-1)} = \frac{2150}{3} \approx 716.67 \]
-
Now use one of the points to find b, by substituting \( m \), \( x \), and \( y \) into the equation \( y = mx + b \). Let's use the point (-1, 10):
\[ 10 = \left(\frac{2150}{3}\right)(-1) + b \] \[ 10 = -\frac{2150}{3} + b \] \[ b = 10 + \frac{2150}{3} \] \[ b = 10 + 716.67 \approx 726.67 \]
-
The final equation of the line in slope-intercept form is: \[ y = \frac{2150}{3}x + 726.67 \]
If you need it in a different format or need help with anything else, feel free to ask!
2 answers