Answer:
[tex]y=75x+150[/tex]
Step-by-step explanation:
Let [tex]y[/tex] represent the number of monitors sold.
Given:
[tex]x[/tex] is the number of years since 1990.
So, for the year 1990, [tex]x=0[/tex].
For the year 2000, 10 years passed. So, [tex]x=10[/tex].
Now, monitors sold in 1990 are 150. So, at [tex]x=0,y=150[/tex]
Monitors sold in 2000 are 900. So, at [tex]x=10,y=900[/tex]
Thus, the two points are [tex](0,150)[/tex] and [tex](10,900)[/tex].
The slope of a line with points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given as:
Slope, [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
For the points [tex](0,150)[/tex] and [tex](10,900)[/tex], the slope is given as:
Slope, [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\ m=\frac{900-150}{10-0}\\ m=75[/tex]
Now, the y-intercept is the point where [tex]x=0[/tex]. So, the point [tex](0,150)[/tex] has [tex]x[/tex] value as 0.
So, the y-intercept is 150.
Equation of a line in slope-intercept form is given as:
[tex]y=mx+b[/tex]
Where, [tex]m[/tex] is the slope and [tex]b[/tex] is the y intercept.
Here, [tex]m=75[/tex] and [tex]b=150[/tex].
Therefore, the equation that represents the above data is given as:
[tex]y=75x+150[/tex]