Question

d two students wrote the equations shown below. erica y = -0.5x aliyah y = 2.5x - 8 10. graphs of both equations will pass through the origin. 11. only erica’s equation is proportional. 12. both equations have a negative slope.

Explanation:

Question 10

Step1: Check Erica's equation

Erica's equation is \( y = -0.5x \). The origin is \((0,0)\). Substitute \( x = 0 \) into the equation: \( y = -0.5(0) = 0 \). So, Erica's graph passes through the origin.

Step2: Check Aliyah's equation

Aliyah's equation is \( y = 2.5x - 8 \). Substitute \( x = 0 \) into the equation: \( y = 2.5(0) - 8 = -8
eq 0 \). So, Aliyah's graph does not pass through the origin.

Step1: Recall proportional equation form

A proportional relationship has the form \( y = kx \) (where \( k \) is a constant) and passes through the origin (\( b = 0 \) in slope - intercept form \( y=mx + b \)).

Step2: Analyze Erica's equation

Erica's equation is \( y=-0.5x \), which is in the form \( y = kx \) with \( k=-0.5 \). So, it is a proportional relationship.

Step3: Analyze Aliyah's equation

Aliyah's equation is \( y = 2.5x-8 \), which is in the form \( y=mx + b \) with \( b=-8
eq0 \). So, it is not a proportional relationship.

Step1: Recall slope - intercept form

The slope - intercept form of a line is \( y = mx + b \), where \( m \) is the slope.

Step2: Find slope of Erica's equation

For Erica's equation \( y=-0.5x \), the slope \( m=-0.5 \), which is negative.

Step3: Find slope of Aliyah's equation

For Aliyah's equation \( y = 2.5x-8 \), the slope \( m = 2.5 \), which is positive.

Answer:

False (the statement is incorrect)

Question 11