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)