Question

Consider the graph of the linear function h(x) = –x + 5. Which could you change to move the graph down 3 units?

Answer 1

We are given linear function h(x) = –x + 5.

On comparing with slope-intercept form y = mx+b, we get b=5.

Therefore, y-intercept is at 5.

We need to change to move the graph down 3 units.

According to rules of transformation f(x)+c shift c units up and f(x)-c shift c units down.

Therefore, in order to  move the graph down 3 units, we need to subtract given function by 3, we get

y = -x+5 -3

y = -x +2.

Here y-intercept is 2.

Therefore, correct option is 3rd option: the value of b to 2.

Answer 2

I don't see a b or an m in this function, but generally, a linear function is of the form ax+b. The b in this equation (not sure if it is the same as your b), controls the shift of the function. Lower b by 3, the graph shifts down by 3.

So unless there is a minus sign before b, it has to be lowered by 3. (If there is a minus sign, it has to be increased by 3).