To find the equation of the line passing through the points (0,6) and (-8,0), you can follow these steps:
1. Calculate the slope (m) of the line using the formula:
\[ m = \frac{y2 - y1}{x2 - x1} \]
Given points (0,6) and (-8,0):
\[ m = \frac{0 - 6}{-8 - 0} = \frac{-6}{-8} = \frac{3}{4} \]
2. Use the point-slope form of the equation of a line:
\[ y - y1 = m(x - x1) \]
Substituting one of the points (0,6) into the equation:
\[ y - 6 = \frac{3}{4}(x - 0) \]
\[ y - 6 = \frac{3}{4}x \]
3. Simplify the equation to get the slope-intercept form (y = mx + b):
\[ y = \frac{3}{4}x + 6 \]
Therefore, the equation of the line passing through the points (0,6) and (-8,0) is:
\[ y = \frac{3}{4}x + 6 \]
This equation represents a line with a slope of 3/4 passing through the given points.
