QuestionVictaria gots prid por wook and $x$ equal the numbar of hours sha works par wook. Givan that the graph shows the sot of all solutions, what is the mathomatical oquation that explains the function? (1 paint) $y=100 x+20 x$ $y=100 z$ $y=100+20 x$ $y=20 x$

Studdy Solution

STEP 1

1. The graph represents a linear relationship between the number of hours worked per week $x$ and the pay $y$ .
2. The line passes through the points $(0, 100)$ and $(40, 900)$ .
3. We need to determine the equation of the line shown in the graph.

STEP 2

1. Identify the slope of the line.
2. Determine the y-intercept of the line.
3. Write the equation of the line in slope-intercept form.

STEP 3

To find the slope $m$ of the line, use the formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ :
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the given points $(0, 100)$ and $(40, 900)$ :
$m = \frac{900 - 100}{40 - 0} = \frac{800}{40} = 20$

STEP 4

The y-intercept $b$ is the value of $y$ when $x = 0$ . From the point $(0, 100)$ , we see that the y-intercept is $b = 100$ .

STEP 5

Using the slope-intercept form of a line $y = mx + b$ , substitute the slope $m = 20$ and the y-intercept $b = 100$ :
$y = 20x + 100$
The mathematical equation that explains the function is:
$\boxed{y = 20x + 100}$

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