Answer:
The equation of the parallel line is y = 5x + 11
Step-by-step explanation:
→ Parallel lines have same slopes and different y-intercepts
→ The slope-intercept form of the linear equation is y = m x + b, where
In our question
∵ The equation of the given line is y = 5x + 2
→ Compare it with the form above to find its slope
∴ m = 5
∵ The two lines are parallel
∴ Their slopes are equal
∴ The slope of the parallel line is 5
→ Substitute it in the form of the equation above
∴ y = 5x + b
→ To find the value of b substitute x and y in the equation by the
coordinates of any point on the line
∵ The line passes through point (-2, 1)
∴ x = -2 and y = 1
∵ 1 = 5(-2) + b
∴ 1 = -10 + b
→ Add 10 to both sides
∴ 1 + 10 = -10 + 10 + b
∴ 11 = b
→ Substitute value of b in the equation
∴ y = 5x + 11
∴ The equation of the parallel line is y = 5x + 11
