Question

select the equations that show a proportional relationship between x and y.
☑️ ( y = 8x + 7 ) ☑️ ( y = 3x )
submit

Explanation:

Step1: Recall proportional relationship form

A proportional relationship between \( x \) and \( y \) is of the form \( y = kx \) (where \( k \) is a constant), meaning it passes through the origin (\( x = 0, y = 0 \)) and has no constant term.

Step2: Analyze \( y = 8x + 7 \)

For \( y = 8x + 7 \), when \( x = 0 \), \( y = 7
eq 0 \). It has a constant term (\( 7 \)), so it is a linear relationship (slope - intercept form \( y = mx + b \) with \( b
eq0 \)) but not proportional.

Step3: Analyze \( y = 3x \)

For \( y = 3x \), when \( x = 0 \), \( y = 0 \), and it is in the form \( y = kx \) (where \( k = 3 \)), so it shows a proportional relationship between \( x \) and \( y \).

Answer:

The equation that shows a proportional relationship between \( x \) and \( y \) is \( y = 3x \). The equation \( y=8x + 7\) does not show a proportional relationship. So the correct selection should be only \( y = 3x \).