Final answer:
To find the equation of a line parallel to the line 2x + 5y - 15 and passing through the point (-10, 1), determine the slope of the given line and use it to write the equation.
Step-by-step explanation:
To find the equation of a line that is parallel to the line 2x + 5y - 15 and passes through the point (-10, 1), we need to find the slope of the given line and use it to write the equation.
- First, let's rearrange the equation of the given line to slope-intercept form (y = mx + b) by isolating y.
- 2x + 5y - 15 = 0 becomes 5y = -2x + 15, then y = (-2/5)x + 3.
- The slope of the given line is -2/5, so the slope of any line parallel to it will also be -2/5.
- Now, we can use the point (-10, 1) and the slope (-2/5) to write the equation of the parallel line using the point-slope form (y - y1 = m(x - x1)).
- Plugging in the values, we get y - 1 = (-2/5)(x + 10).
- Simplifying the equation, we have y - 1 = (-2/5)x - 4.
- Finally, rearranging the equation gives us the equation of the line parallel to the given line and passing through the point (-10, 1): y = (-2/5)x - 3.