Write a linear function g with the given values. g\left(0\right)=9 , g\left(8\right)=7

Answer 1

Since g(0) = 9, the point (0,9) is on the line.

Since g(8) = 7, the point (8,7) is also on the line.

Slope = (9 - 7) / (0 - 8) = 2 / (-8) = -1/4

Equation of line: y - 7 = (-1/4)(x - 8)

y - 7 = (-1/4)x + 2

So, y = (-1/4)x + 9.

Answer 2

A linear function g(x) is often written in slope-intercept form: y = mx + b. In this format, the y value is equivalent to g(x), m is the slope, and b is the y-intercept.

Some notes on format and substitutions to start:

g(x) = y

g(0) = b = y-intercept

m = slope = (y₂-y₁)/(x₂-x₁) for two points (x₁,y₁) and (x₂,y₂)

The y-intercept is the y-coordinate for x = 0. We already know g(0) = 9, so for x = 0, y = 9. Therefore, the y-intercept is 9, so b is 9.

Our updated linear function is y = mx + 9. So now, we need to find the slope.

Two points we have are (0,9) and (8,7). For two points, their slope is the difference in y values divided by the difference in x values, so we have m = (7-9)/(8-0) = (-2)/8 = -1/4. Now we have the slope.

Putting it all together, we have the answer: y = (-1/4)x + 9

Answer 3

Use y = mx + b with m the slope and b the y intercept.

g(0) = 9

Plug in 0 for x and 9 for y.

9 = m(0) + b

b = 9

The equation is y = mx + 9

Plug in the second point to find m.

g(8) = 7 is (8,7)

7 = m*8 + 9

-2 = 8m

-1/4 = m

y = (-1/4)x + 9