Question

Rewrite the explicit formula in function form. The identify the y

intercept of the function.
an = 9-3(n-1)

Answer 1

Answer: y-intercept: (0, 12)

Explanation:

`a_n` = 9 − 3 (n − 1)

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Find the values of m and b using the form y = mx + b.

m = −3

b = 12

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: −3

intercept: (0, 12)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.

Find the x-intercept.

To find the x-intercept(s), substitute in 0 for y and solve for x.

0 = −3x + 12

Solve the equation.

Rewrite the equation as −3x + 12 = 0.

−3x + 12 = 0

Subtract 12 from both sides of the equation.

−3x = −12

Divide each term by −3 and simplify.

x = 4

x-intercept(s) in point form.

x-intercept(s): (4, 0)

Find the y-intercept.

To find the y-intercept(s), substitute in 0 for x and solve for y.

y = −3 ⋅ 0 + 12

Solve the equation.

Remove parentheses.

y = −3 ⋅ 0 + 12

Simplify −3 ⋅ 0 + 12.

y = 12

intercept(s) in point form.

intercept(s): (0, 12)

Create a table of the x and y values.

x | y

0 | 12

4 | 0

Graph the line using the slope and the y-intercept, or the points.

Slope: −3

intercept: (0, 12)