Answer :
To determine which graph matches the equation \( y + 3 = 2(x + 3) \), let's transform this equation into slope-intercept form \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept.
1. Start with the original equation:
[tex]\[ y + 3 = 2(x + 3) \][/tex]
2. Distribute the 2 on the right-hand side:
[tex]\[ y + 3 = 2x + 6 \][/tex]
3. Isolate \( y \) by subtracting 3 from both sides:
[tex]\[ y = 2x + 3 \][/tex]
Now we have the equation in slope-intercept form \( y = 2x + 3 \). From this equation, we can identify the slope and the y-intercept:
- The slope \( m \) is 2.
- The y-intercept \( b \) is 3.
Given these values, the graph that matches the equation \( y + 3 = 2(x + 3) \) is a straight line with a slope of 2 and a y-intercept at 3. This means the line will intersect the y-axis at the point (0, 3) and will rise 2 units for every 1 unit it goes to the right.
Therefore, the correct graph will display a line with these characteristics.
1. Start with the original equation:
[tex]\[ y + 3 = 2(x + 3) \][/tex]
2. Distribute the 2 on the right-hand side:
[tex]\[ y + 3 = 2x + 6 \][/tex]
3. Isolate \( y \) by subtracting 3 from both sides:
[tex]\[ y = 2x + 3 \][/tex]
Now we have the equation in slope-intercept form \( y = 2x + 3 \). From this equation, we can identify the slope and the y-intercept:
- The slope \( m \) is 2.
- The y-intercept \( b \) is 3.
Given these values, the graph that matches the equation \( y + 3 = 2(x + 3) \) is a straight line with a slope of 2 and a y-intercept at 3. This means the line will intersect the y-axis at the point (0, 3) and will rise 2 units for every 1 unit it goes to the right.
Therefore, the correct graph will display a line with these characteristics.
