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What is the equation of a line with a slope of 6 and a [tex]\( y \)[/tex]-intercept of -2?

A. [tex]\( y = -2x + 6 \)[/tex]
B. [tex]\( y = 6x - 2 \)[/tex]
C. [tex]\( y = 6x + 2 \)[/tex]
D. [tex]\( y = 2x + 6 \)[/tex]

Sagot :

GinnyAnswer
To determine the equation of a line, we use the slope-intercept form of the equation, which is given by:

[tex]\[ y = mx + b \][/tex]

where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept, which is the point where the line crosses the y-axis.

In this problem, we are provided with:
- A slope [tex]\( m = 6 \)[/tex].
- A y-intercept [tex]\( b = -2 \)[/tex].

Following the formula [tex]\( y = mx + b \)[/tex], we substitute the given values:

1. Substitute [tex]\( m \)[/tex] with 6:
[tex]\[ y = 6x + b \][/tex]

2. Then, substitute [tex]\( b \)[/tex] with -2:
[tex]\[ y = 6x - 2 \][/tex]

Thus, the equation of the line is:
[tex]\[ y = 6x - 2 \][/tex]

Therefore, the correct answer is:

B. [tex]\( y = 6x - 2 \)[/tex]
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