Question

example 3) solve $-2x + 6 = -2(x - 3)$ by graphing.
equation 1:
$square$ the $y$-intercept is
$square$ the slope is
equation 2:
$square$ the $y$-intercept is
$square$ the slope is
answer:

Explanation:

Step1: Simplify Equation 1

The first equation is \( y = -2x + 6 \). In the slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For \( y=-2x + 6 \), the slope \( m=-2 \) and the y - intercept \( b = 6 \).

Step2: Simplify Equation 2

Expand the second equation \( y=-2(x - 3) \). Using the distributive property \( a(b - c)=ab-ac \), we get \( y=-2x+6 \). In the slope - intercept form \( y = mx + b \), the slope \( m=-2 \) and the y - intercept \( b = 6 \).

Step3: Analyze the graphs

Since both equations \( y=-2x + 6 \) and \( y=-2x + 6 \) are identical, their graphs are the same line. This means that the system of equations (even though it's a single equation in two forms here) has infinitely many solutions, and the two lines (which are the same line) coincide.

Answer:

Equation 1: The y - intercept is \( 6 \), The slope is \( - 2 \)
Equation 2: The y - intercept is \( 6 \), The slope is \( - 2 \)
The two equations represent the same line, so there are infinitely many solutions (all points on the line \( y=-2x + 6 \)).