The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB in slope-intercept form that contains point?

y = 2 x + b

Use whatever point they gave you to find b

To find the equation of a line parallel to line AB, we need to use the slope-intercept form of a linear equation, which is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept.

In this case, line AB has a slope of 2. Since parallel lines have the same slope, the line we want to find will also have a slope of 2.

Now, we need to find the y-intercept (b) for the line passing through a given point. Let's assume the given point is (x1, y1).

To calculate the y-intercept (b), we can substitute the coordinates of the given point (x1, y1) into the equation y = mx + b and solve for b.

Using the equation y = 2x + 4 and the given point (x1, y1), we can write the equation as:

y1 = 2x1 + b

Now we can solve for b:

b = y1 - 2x1

Using the value of b, we can write the equation of the line in slope-intercept form:

y = 2x + (y1 - 2x1)

Therefore, the equation of a line parallel to line AB in slope-intercept form that contains the point (x1, y1) is:

y = 2x + (y1 - 2x1)