Question

A student earns a 98 on a test for answering one question incorrectly and earns a 90 for answering five questions incorrectly. Is the slope of the line that models the linear relationship a positive negative zero or undefined slope?

Answer 1

Negative Slope

Explanation:

The slope is the ratio of Change in height to the change in horizontal distance. It can also be define as tangent of angle made by that line and it is find by formula,
`slope (m)= (y_(2) - y_(1))/(x_(2) - x_(1))`

The slope is said to be a positive slope when a line is moving from left to right, the line rises.

The slope is said to be a negative slope when a line is moving from left to right, the line falls.

Here, Let the student earns be y marks in test

and let incorrect question be x

then y₁ = 98 , y₂ = 90 and x₁ = 1 , x₂ = 5

then
`slope (m)= (y_(2) - y_(1))/(x_(2) - x_(1))`

`slope (m)= (90 - 98)/(5 - 1)`

⇒ m = -2

Hence, it has negative slope.

Answer 2

This can be solved by solving the slope of the line. First let y be the rating of the test and x be the number of incorrect answers. Slope can be solved using the formula:

M = ( y2 – y1 ) / ( x2 – x1)

M = ( 90 – 98) / ( 5 -1 )

M = -2

So the model has a negative slope