Final answer:
The equation of the line parallel to y=1/2x-3 and passing through the point (4,10) is y=1/2x+8.
Step-by-step explanation:
The question is asking for the equation of a line that is parallel to a given line and passes through a specific point (4,10). The given line has the equation y=1/2x-3. Since parallel lines have the same slope, our unknown equation will have the same slope, which in this case is 1/2.
To find the equation of the line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line (which we know is (4,10)) and m is the slope (which is 1/2).
Substituting the point and slope into the point-slope form gives:
y - 10 = 1/2(x - 4)
To put this into slope-intercept form (y = mx + b), we simplify:
- y - 10 = 1/2x - 2
- Add 10 to both sides to get the y-intercept:
- y = 1/2x + 8
So, the equation of the parallel line that goes through the point (4, 10) is y=1/2x+8.