Exercise 39 Page 176

Let's begin by sketching their graphs. The first graph has a slope of $2$ and a $y\text{-}$intercept of $0.$ To draw the second graph, we will write it in slope-intercept form. The second graph also has a slope of $2$ but a $y\text{-}$intercept of $7.$ Let's graph this stuff! If we recall the chapter on transformations, we know that: By rewriting the general point-slope form, we can relate it to these types of transformations. We see that point-slope form represents a horizontal translation by $h$ and a vertical translation by $k$ of the function $y=mx.$ Let's substitute $k=1$ and $h=\text{-}3$ into this general equation and simplify This means $y-1=2(x+3)$ is a translation of $3$ units to the left and $1$ unit up of the function $y=2x.$ Let's show this below.