When lines are parallel, they have the same slope.
y= - 2x+ 3
Because of this, we know that all lines that are parallel to our given line will have a slope of - 2. This means we can write a general equation in slope-intercept form for all lines parallel to the given equation.
y= - 2x+ b
We are asked to write the equation of a line parallel to the given equation that passes through the given point (0, - 1). This point is the y-intercept of the parallel line. In this case, we do not need to perform any further calculations to find the value of b.
y= - 2x+( - 1) ⇔ y=- 2x-1
Finally, we can verify our answer by graphing both lines on the same coordinate plane. If they are parallel, they will never intersect.
We can see by looking at the graphs of the functions that they are indeed parallel.
