Let's analyze the transformation from Line A [tex]\( y = 5x - 7 \)[/tex] to Line B [tex]\( y = 2x + 3 \)[/tex].
### Step-by-Step Solution:
1. Identify the slope and y-intercept of Line A:
- The equation for Line A is [tex]\( y = 5x - 7 \)[/tex].
- The slope (the coefficient of [tex]\( x \)[/tex]) is [tex]\( 5 \)[/tex].
- The y-intercept (the constant term) is [tex]\( -7 \)[/tex].
2. Identify the slope and y-intercept of Line B:
- The equation for Line B is [tex]\( y = 2x + 3 \)[/tex].
- The slope is [tex]\( 2 \)[/tex].
- The y-intercept is [tex]\( 3 \)[/tex].
3. Calculate changes in slope and y-intercept:
- The change in slope is the difference between the slope of Line B and the slope of Line A:
[tex]\[
\text{Change in slope} = 2 - 5 = -3
\][/tex]
- The change in y-intercept is the difference between the y-intercept of Line B and the y-intercept of Line A:
[tex]\[
\text{Change in y-intercept} = 3 - (-7) = 3 + 7 = 10
\][/tex]
Hence, the new slope is [tex]\( 2 \)[/tex], and the line is shifted such that the y-intercept changes by [tex]\( 10 \)[/tex] units upwards.
