Question

The table of vaules represents a linear function g(x) where X is the number of days that have passed and g(x) is the blance in the bank account x vaules 0,3,6 G(x) vaules $600,$720,840
Part A Find the interpert the slope of the function

Part B write equation of the line in point slope, slope - intercept and standard forms

Part C write equation of the line using function notation

Answer 1

Answer:

Step-by-step explanation:

The slope formula is

$m=\frac{y_2-y_1}{x_2-x_1}$

Filling in this formula with 2 different points 2 times will ensure that this is fact a linear function. In other words, if the slope comes up the same between points 1 and 2 and then between points 2 and 3, this is linear.

Between (0, 600) and (3, 720) the slope formula is

$m=\frac{720-600}{3-0}=\frac{120}{3}=40$  and

$m=\frac{840-720}{6-3}=\frac{120}{3}=40$ So this is in fact linear because the slopes are the same.

Interpreting a slope is similar to interpreting a unit ratio. In our case, the slope means that after the initial investment in the account, $40 per day (there's the unit rate I was referring to) is deposited into the account.

Using that slope to write first the point-slope form of the line allows us to use any one of the 3 coordinates to write the equation. I use (0, 600). In point-slope form:

$y-600=40(x-0)$

That's point-slope form. Now for slope-intercept form, which is the same as solving for y.

y - 600 = 40x - 0 and

y = 40x + 600. That's slope-intercept, and now for standard form. Standard form follows the format of a. No fractions and b. Both the x and y terms go on the same side of the equals sign and the constant on the other.

We move the x term over to the y side:

-40x + y = 600. But a lot of textbooks don't like to lead with a negative, so the equivalent form of this with a positive leading coefficient is

40x - y = -600 (notice that all we did was change ALL the signs to the opposite of what they were, not just the sign on the x term. Very important!!)