Question

What is the equation of the line that passes through the point (4,5) and is parallel to the line whose equation is y=(4/5)x-4

Answer 1

To find the equation of a line parallel to y = (4/5)x - 4 and passing through the point (4,5), we keep the slope the same, which is 4/5, and solve for the new y-intercept using the point (4,5), yielding the equation y = (4/5)x + 9/5.

Step-by-step explanation:

The equation of a line that is parallel to another has the same slope, which is the coefficient of x in the equation y = mx + b, where m represents the slope and b represents the y-intercept. The given line whose equation is y = (4/5)x - 4 has a slope of 4/5. To find the equation of a line parallel to this line and passing through the point (4,5), maintain the same slope but solve for the new y-intercept using the point-slope form, which is y - y1 = m(x - x1) where (x1, y1) is a point on the line.

Step-by-step solution:

1. Since the slope must be the same, the new line will have the form y = (4/5)x + b.
2. Plug the coordinates of the given point (4,5) into the equation and solve for b: 5 = (4/5)*4 + b, which simplifies to 5 = 16/5 + b.
3. Subtracting 16/5 from both sides to solve for b yields b = 25/5 - 16/5 = 9/5.
4. The equation of the line that is parallel to y = (4/5)x - 4 and passes through the point (4,5) is therefore y = (4/5)x + 9/5.