Question

11
mark for review
( y = 2x + 10 )
( y = 2x - 1 )
at how many points do the graphs of the given equations intersect in the ( xy )-plane?
a zero
b exactly one
c exactly two
d infinitely many

Explanation:

Step1: Recall slope-intercept form

The equations are in \( y = mx + b \) form, where \( m \) is slope and \( b \) is y - intercept. For \( y = 2x+10 \), slope \( m_1 = 2 \), y - intercept \( b_1 = 10 \). For \( y = 2x - 1 \), slope \( m_2=2 \), y - intercept \( b_2=- 1 \).

Step2: Analyze parallel lines

If two lines have the same slope (\( m_1=m_2 \)) and different y - intercepts (\( b_1
eq b_2 \)), they are parallel. Parallel lines in the xy - plane never intersect. So we set the two equations equal to each other: \( 2x + 10=2x-1 \). Subtract \( 2x \) from both sides: \( 10=-1 \), which is a false statement, meaning no solution for \( x \), so no intersection points.

Answer:

A. Zero