Question

21. Randy owns a computer store. In 1990, he sold 150 monitors. In 2000, he sold 900

Answer 1

Answer:

$y=75x+150$

Step-by-step explanation:

Let $y$ represent the number of monitors sold.

Given:

$x$ is the number of years since 1990.

So, for the year 1990, $x=0$.

For the year 2000, 10 years passed. So, $x=10$.

Now, monitors sold in 1990 are 150. So, at $x=0,y=150$

Monitors sold in 2000 are 900. So, at $x=10,y=900$

Thus, the two points are $(0,150)$ and $(10,900)$.

The slope of a line with points $(x_{1},y_{1})$ and $(x_{2},y_{2})$  is given as:

Slope, $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

For the points $(0,150)$ and $(10,900)$, the slope is given as:

Slope, $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\ m=\frac{900-150}{10-0}\\ m=75$

Now, the y-intercept is the point where $x=0$. So, the point $(0,150)$ has $x$ value as 0.

So, the y-intercept is 150.

Equation of a line in slope-intercept form is given as:

$y=mx+b$

Where, $m$ is the slope and $b$ is the y intercept.

Here, $m=75$ and $b=150$.

Therefore, the equation that represents the above data is given as:

$y=75x+150$