Question

$\text{Function 1:}\frac{5}{2}w+3$
From the following, has a greater slope and a higher y-intecept value than function 1.

• A. y = 2w + 2
• B. y = 3w + 2
• C. y = 2w + 5
• D. y = 3w + 5

Answer 1

The correct option is D y = 3w + 5

$\text{Equation of Function 1:}\frac{5}{2}w+3$

$\text{The above equation is in the form of y = mx + c}$

We know in the equation y = mx + c, "m" indicates the slope which also shows the rate of change of a function.

$\text{So, compare the equation y =}\frac{5}{2}\text{w + 3}$
$\text{with y = mx + c, we observe:}$

$\text{Slope = rate of change of A =}\frac{5}{2}=2.5$

Here, value of y-intercept = 3

So we have to search for those equations representing a function with slope greater than 2.5 and y-intercept value greater than 3.

In the equation y = 3w + 5, we see:
Value of y-intercept value = 5
Value of slope (m) = 3

In the equation y = 2w + 5, we see:
Value of y-intercept value = 5
Value of slope (m) = 2

In the equation y = 2w + 2, we see:
Value of y-intercept value = 2
Value of slope (m) = 2

In the equation y = 3w + 2, we see:
Value of y-intercept value = 2
Value of slope (m) = 3

∴ Only the equation y = 3w + 5 have a greater slope and higher y-intercept value than the equation representing Function 1.

$\text{So, the correct choice is}y=3w+5$