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Line A [tex]\([ y = 5x - 7 ]\)[/tex] is transformed into Line B [tex]\([ y = 2x + 3 ]\)[/tex].

Which best describes the new slope and [tex]\( y \)[/tex]-intercept?

The new slope is [tex]\(\square\)[/tex], and the [tex]\( y \)[/tex]-intercept is shifted to [tex]\(\square\)[/tex].

Sagot :

GinnyAnsweridn
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.
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