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
∵ 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
∴ [tex]\frac{3y}{3}=\frac{4}{3}-\frac{1}{3}x[/tex]
∴ y = [tex]\frac{4}{3}[/tex] - [tex]\frac{1}{3}[/tex] x
→ Compare it with the form of the equation above
∴ m = [tex]-\frac{1}{3}[/tex]
∵ Parallel lines have the same slopes
∴ The slope of the parallel line is [tex]-\frac{1}{3}[/tex]
→ Put it in the form of the equation
∴ y = [tex]-\frac{1}{3}[/tex] 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 = [tex]-\frac{1}{3}[/tex] (2) + b
∴ 5 = [tex]-\frac{2}{3}[/tex] + b
→ Add [tex]\frac{2}{3}[/tex] to both sides
∴ [tex]\frac{17}{3}[/tex] = b
→ Substitute it in the form of the equation above
∴ y = [tex]-\frac{1}{3}[/tex] x + [tex]\frac{17}{3}[/tex]
→ 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
Answer:
[tex]\displaystyle y-5=-\frac{1}{3}(x-2)[/tex]
Step-by-step explanation:
Equation of a Line
Two lines are parallel if they have the same slope. We are given the equation of the line:
x+3y=4
To find the slope of this line, we must solve for y:
[tex]\displaystyle y=-\frac{1}{3}x+\frac{4}{3}[/tex]
The slope of this line is:
[tex]\displaystyle -\frac{1}{3}[/tex]
The equation of the new line has the same slope. To find its equation, we use the point-slope form of the line:
y-k=m(x-h)
Where (h,k)=(2,5). Thus:
[tex]\boxed{\displaystyle y-5=-\frac{1}{3}(x-2)}[/tex]
