Step 1a

To find the equation of the linear function g(x) given its slope m and a point \$(x_1, y_1)\$ it passes through, you can use the point-slope form of a linear equation:

\$y - y_1\$ = \$m(x - x_1)\$

Using the given information, we have:

g(x) = y

m = 5 (slope), \$x_1 = 5\$, \$y_1 = 9\$.

Explanation: Here, we consider the points are (5,9) is \$(x_1,y_1)\$ and slope(m) = 5.

Step 1b

Substituting these values in the formula:

y - 9 = 5(x - 5)

Now, let’s simplify and solve for y to obtain the equation of the linear function:

y - 9 = 5x - 25

Add 9 to both sides:

y = 5x − 25 + 9

y = 5x − 16

So, the equation of the linear function g(x) = 5x − 16.

Explanation: Here, substituted values into the formula then we get g(x) = 5x - 16.