Write an equation for the line parallel to the given line y = 4x + 5 that contains c = 7.

Solution:

Parallel lines have the same slope and but not the same intercept value.

Using the general equation of the line, i.e. y = mx + c, where m is the slope of the line and c is the y-intercept.

Since the line y = 4x + 5 is parallel to the required line, their slopes must be equal.

Thus, m = 4

Given, c = 7

Substitute the values of m and c in the general equation of the line to get the required equation,

⇒ y = 4x + 7

Thus, y = 4x + 7 is the equation for the line parallel to the given line y = 4x + 5 that contains c = 7.

Write an equation for the line parallel to the given line y = 4x + 5 that contains c = 7.

Summary:

y = 4x + 7, is an equation for the line parallel to the given line y = 4x + 5 that contains c = 7.