Final answer:
To find the equation of a line parallel to another, use the same slope and the point it passes through to solve for the y-intercept. For y = 2/3x + 1 and point (4,5), the parallel line's equation is y = 2/3x + 7/3.
Step-by-step explanation:
To find the equation of a line parallel to another line, you need to use the same slope since parallel lines have identical slopes. For example, if you have an initial equation y = 2/3x + 1, here the slope (m) is 2/3. A line parallel to this would also have a slope of 2/3.
Next, since the new line needs to pass through a specific point, say (4,5), you'd use the slope-intercept form of the equation y = mx + b and plug in the slope and this point to solve for the y-intercept (b).
Insert the slope (2/3) and the point (4,5) into the equation:
- 5 = (2/3)(4) + b
- 5 = 8/3 + b
- b = 5 - 8/3
- b = 15/3 - 8/3
- b = 7/3
So, the equation for the line parallel to y = 2/3x + 1 that passes through the point (4,5) is y = 2/3x + 7/3.