Question

Consider the line whose equation is y=2x-3. We would like to find its equation after translating it 4 units left and 5 units up. (a) What is the slope of the new line? Why?(b) The y-intercept of the original line was at (0,-3). What is its image point under this translations?(c) using the point from (b) and (a), write the equation of the image line using point-slope form.

Answer 1

The new function is

`\begin{gathered} y+5=2(x+4)-3 \\ y=2x+8-3-5=2x \end{gathered}`

a) the slope is the same, because the translation does not affect the slope.

b) the new image of (0,-3) is (4,2)

c) the equation is y=2x