Question

Examine the linear relationships.

Linear equation A: y=45x
Linear equation B is represented by this graph.


A line that passes through points (0, 2) and (5, 4).

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Which statement is entirely correct?

Equation A has a steeper slope, because 45 is greater than 25.Equation A has a steeper slope, because 4 fifths is greater than

Equation B has a steeper slope, because 45 is greater than 25.Equation B has a steeper slope, because 4 fifths is greater than

Equation A has a steeper slope, because 52 is greater than 45.Equation A has a steeper slope, because 5 halves is greater than

Equation B has a steeper slope, because 52 is greater than 45.

Answer 1

Using linear functions, it is found that the correct option is:

Equation A has a steeper slope, because $\frac{4}{5}$ is greater than $\frac{2}{5}$.

A linear function has the following format:

$y = ax + b$

In which:

• a is the slope, which is the rate of change.

• The higher the slope, the steeper the function is:

Linear equation A is given by:

$y = \frac{4}{5}x$

Linear equation B passes through points (0, 2) and (5, 4). Since the slope between two points is given by change in y divided by change in x, we have that:

$m = \frac{4 - 2}{5 - 0} = \frac{2}{5}$

Equation A has a higher slope, hence, it is steeper, and the correct option is:

Equation A has a steeper slope, because $\frac{4}{5}$ is greater than $\frac{2}{5}$.

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