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Which of the following is the equation of a line in slope-intercept form for a line with slope [tex]\(5\)[/tex] and [tex]\(y\)[/tex]-intercept at [tex]\((0,-3)\)[/tex]?

A. [tex]\(y = 5x + 3\)[/tex]
B. [tex]\(y = 5x - 3\)[/tex]
C. [tex]\(x = 3y - 5\)[/tex]
D. [tex]\(y = -3x + 5\)[/tex]

Sagot :

GinnyAnswer
To find the equation of a line in slope-intercept form, we start by understanding the slope-intercept form itself, which is given by:

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

Here:
- [tex]\(m\)[/tex] is the slope of the line.
- [tex]\(b\)[/tex] is the y-intercept, which is the value of [tex]\(y\)[/tex] when [tex]\(x\)[/tex] is 0.

Given the problem:
- The slope ([tex]\(m\)[/tex]) is 5.
- The y-intercept ([tex]\(b\)[/tex]) is -3.

Substitute these values into the slope-intercept form equation:

[tex]\[ y = 5x + (-3) \][/tex]

This simplifies to:

[tex]\[ y = 5x - 3 \][/tex]

Now, let's compare this equation with the provided options:

A. [tex]\( y = 5x + 3 \)[/tex]

B. [tex]\( y = 5x - 3 \)[/tex]

C. [tex]\( x = 3y - 5 \)[/tex]

D. [tex]\( y = -3x + 5 \)[/tex]

The correct equation from the comparison is:

[tex]\[ \boxed{y = 5x - 3} \][/tex]

Hence, the correct option is:

[tex]\[ \boxed{B} \][/tex]
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