Final answer:
To find an equation of a line parallel to y = 7 - 4x, we need to determine the slope of the given line first. The equation of the parallel line can be written as y = -4x + b, where b is the y-intercept. Substituting the coordinates of a point that the line passes through allows us to solve for b and obtain the equation of the parallel line.
Step-by-step explanation:
To find an equation of a line parallel to y = 7 - 4x, we need to determine the slope of the given line first. The equation is in slope-intercept form y = mx + b, where m is the slope. In this case, the slope is -4.
Since parallel lines have the same slope, the equation of the parallel line can be written as y = -4x + b. To find the value of b, we can substitute the coordinates of a point that the line passes through. Let's use the point (-3, 1) in this case.
Substituting the values into the equation, we get 1 = -4(-3) + b. Simplifying gives us 1 = 12 + b. To solve for b, we subtract 12 from both sides, giving us b = -11.
Therefore, the equation of the line that is parallel to y = 7 - 4x and passes through the point (-3, 1) is y = -4x - 11.