I need help please😭

Question

Find a linear function h, given h(5)=-1 and h(-2)=13

Answer 1

The fact that h(5) = -1 is similar to stating that in an x-y coordinate plane the function passes through (5, -1).

Similarly the function passes through (-2, 13).

So, how to you find the equation of a line (the function is given to be linear) when you know two points?

1. Find the slope of the line using m = (y₂-y₁)/(x₂-x₁).
2. Use point-slope (or slope-intercept) form to write the equation.
3. Use function notation to write the equation for h(x).

m = 14/-7 = -2

Using point-slope:

y - 13 = -2 (x+2) (could have used either point as (x₁,y₁))

y = -2x-4+13

y = -2x+9

h(x) = -2x+9

h(5) = -10+9=-1

h(-2) = 4+9=13

Take a look at this Desmos graph to see how you can do these calculations there:

desmos.com/calculator/rsrbe8yf8n