The instructor had saved $3,500 and rents an apartment for $275 monthly. He believes the point (6, 1850) would be on the equation of the line. Is he correct? Explain how to check if a point is on a line.
Answers
Answer: Write the equation using slope and y-intercept in slope-intercept form, y = –275x + 3500. Then, substitute the x and y values of the point into the equation, 1850 = –275(6) + 3500. Simplify to see if both sides are equivalent. Yes, the instructor is correct because both sides are equivalent.
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SOLUTION
GIVEN
- The instructor had saved $ 3,500 and rents an apartment for $ 275 monthly.
- He believes the point (6, 1850) would be on the equation of the line.
TO DETERMINE
Is he Correct ? Explain how to check if a point is on a line.
EVALUATION
Let the instructor has to pay rent of the apartment for x months
Also let the money left = $ y
So rent for x months = $ 275x
So by the given condition
y = 3500 - 275x
∴ 275x + y = 3500
Which is the required equation of the line
Now we have to check whether (6,1850) lies on the line
The equation of the line is
275x + y = 3500
Putting x = 6 , y = 1850 we get
( 275 × 6 ) + 1850 = 3500
⇒ 1650 + 1850 = 3500
⇒ 3500 = 3500
Which is true
Hence (6,1850) lies on the line
We can also check it on the graph that the point A(6,1850) lies on the line
Graph : Graph is referred to the attachment
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