Answer:
The equation of the parallel line is x + 3y = 17
Step-by-step explanation:
Parallel lines have the same slopes and different y-intercept
The form of the equation y = m x + b, where
- m is the slope of the line
- b is the y-intercept
∵ The equation of the given line is x + 3y = 4
→ We must put it in the form above to find its slope
→ Subtract x from both sides to move x to the right side
∵ x - x + 3y = 4 - x
∴ 3y = 4 - x
→ Divide both sides by 3 to make the coefficient of y = 1
∴
∴ y = -
x
→ Compare it with the form of the equation above
∴ m =
∵ Parallel lines have the same slopes
∴ The slope of the parallel line is
→ Put it in the form of the equation
∴ y = x + b
→ To find b substitute x and y in the equation by the coordinates
of a point on the line
∵ The line passes through the point (2, 5)
∴ x = 2 and y = 5
→ Substitute them in the equation
∴ 5 = (2) + b
∴ 5 = + b
→ Add to both sides
∴ = b
→ Substitute it in the form of the equation above
∴ y = x +
→ Multiply each term by 3
∴ 3y = - x + 17
→ Add x to both sides
∴ x + 3y = 17
∴ The equation of the parallel line is x + 3y = 17