Exercise 39 Page 176

Let's begin by sketching their graphs. The first graph has a slope of 2 and a y-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-intercept of 7. Let's graph this stuff!

If we recall the chapter on transformations, we know that: Horizontal Translation:& f(x-h) Vertical Translation:& f(x)+k By rewriting the general point-slope form, we can relate it to these types of transformations. y-k=m(x-h) ⇔ y=m(x-h)+k 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=- 3 into this general equation and simplify

y=m(x-h)+k

SubstituteII

h= - 3, k= 1

y=m(x-( - 3))+ 1

SubNeg

a-(- b)=a+b

y=m(x+3)+1

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.