Final answer:
To write an equation parallel to x - 2y = 14 and passing through (4, 5), we need to find the slope of the given equation and use it to write the new equation y = 0.5x - 2.
Step-by-step explanation:
Step by step explanation:
- First, rearrange the given equation in the slope-intercept form (y = mx + b), where m is the slope: x - 2y = 14 becomes -2y = -x + 14, then divide by -2 and simplify to get y = 0.5x - 7.
- The slope of the given equation is 0.5.
- Since parallel lines have the same slope, the new equation will have a slope of 0.5.
- Using the point-slope form of a linear equation, y - y1 = m(x - x1), substitute the coordinates of the given point (4, 5), and the slope (0.5) into the equation.
- Simplifying the equation, you get y - 5 = 0.5(x - 4), which can be further simplified to the final equation y = 0.5x - 2.