Find a linear function h, given h(5)=-7 and h(-1)=11. Then find h(8)

Question

Find

Answer 1

Hi Madi,

To answer your question first remember that every linear function has the form:

y = h(x) = mx + b

where m is the slope of the line and b is the y-intercept.

Given two points on a line we can determine the slope of the line that passes through these points using the slope formula

m = (y_2 - y_1)/(x_2 - x_1)

we are given that (5,-7) and (-1,11) are points on this line so if we let x_1 = 5 and x_2 = -1 and y_1 = -7 and

y_2 = 11 and plug this into the slope equation we find that

m = (11-(-7))/(-1 - 5) = 18/-6 = -3

So h(x) = -3x + b

b can be found by just plugging in one of the pairs of points. Try (5,-7). Because this is a point on the line, we know that

-7 = h(5) = -3(5) + b

-3(5) + b = -7

so

-15 + b = -7

b = 8

so h(x) = -3x + 8. To find h(8) we plug x = 8 into this equation and see that h(8) = -3(8) + 8 = -16

so h(8) = -16

Hope this helps!

Answer 2

Stawrt with two-point form

(y + 7) / (x - 5) = (11 + 7) / (-1 - 5)

Can you simplify and and answer?