Final answer:
To find the equation of a line parallel to 5x - 2y = 12 that passes through (-10, 3), first determine the slope, which is 5/2. Use the point-slope form with this slope and the given point to find the new line's equation: y = (5/2)x + 28.
Step-by-step explanation:
The equation of the line passing through the point (-10, 3) that is parallel to the line 5x - 2y = 12 can be found by determining the slope of the given line and using the point-slope form of a linear equation.
Step-by-step solution:
- First, rearrange the given equation in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
- To find the slope of the given line, solve the equation for y to get y = (5/2)x - 6. The slope of the given line is 5/2.
- Since the line we want to find is parallel, it will have the same slope. Therefore, the slope of the line we want to find is also 5/2.
- Now, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
- Plugging in (-10, 3) as the point and 5/2 as the slope, we have y - 3 = (5/2)(x - (-10)).
- Simplifying the equation, we get y - 3 = (5/2)(x + 10).
- Expanding the right side of the equation, we have y - 3 = (5/2)x + 25.
- Finally, rearrange the equation to get the slope-intercept form, which is y = (5/2)x + 28.
Therefore, the equation of the line passing through the point (-10, 3) and parallel to the line 5x - 2y = 12 is y = (5/2)x + 28.