Given the equation y=-5x+8 how will y change if x increases by 6 units?

Answer 1

Another method of solving:

To determine where this linear equation intersects the y-axis, you can substitute 0 for x and the equation then reads:

y = -5(0)+8 

y = 8

Now substitute +6 for x and the equation now reads:

y = -5(+6) + 8

y = -30+8

y = -22

(0,8)

(6,-22)

These two points show that when x increases from 0 to 6, y decreases from +8 to -22. A number line will show a decrease of 30 units as you move along the number line from a positive 8 to a negative 22.

Answer 2

The equation y=-5x+8 is in the form y=mx+b, with m=-5 and b=8. If x increases by 6 units, the equation will become y=-5(x+6)+8, which expands to y=-5x-30+8 and simplifies to y=-5x-22. The difference between the original equation and the modified equation is the constant variable "b" from the general equation y=mx+b, which is now 30 units lower than the original equation.