The salaries will be the same in year 20 and she will be earning $80,000. So, the first option is correct.
The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
We will first create an equation to represent the data.
To find the slope we use the formula
m = (y₂-y₁)/(x₂-x₁)
= (60,000-55,000) / (12-10)
= 5,000/2 = 2500
Writing this in point-slope form, we have
y-y₁ = m(x-x₁)
y-55,000 = 2500(x-10)
Converting to slope-intercept form,
y-55,000 = 2500 × x - 2500 × 10
y - 55,000 = 2500x - 25,000
y = 2500x + 30,000
Now we set this equal to the equation from the graph:
2500x + 30,000 = 2000x + 40,000
Subtract 2000x from both sides:
2500x + 30,000 - 2000x = 2000x + 40,000 - 2000x
500x + 30,000 = 40,000
500x = 40,000 - 30,000
500x = 10,000
x = 10,000/500
x = 20
The salaries will be the same in year 20.
y= 2000(20) + 40,000
y= 40,000 + 40,000
= 80,000
The salary in year 20 will be $80,000.
Learn more about a point-slope form;
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