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

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

Sagot :

Certainly! Let's solve the problem step-by-step.

1. Understand the Slope-Intercept Form:
- The equation of a line in slope-intercept form is given by [tex]\( y = mx + b \)[/tex].
- Here, [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept, i.e., the point where the line crosses the y-axis.

2. Identify Given Values:
- We are given the slope [tex]\( m = 5 \)[/tex].
- We are also given the y-intercept as the point [tex]\( (0, -3) \)[/tex]. This means [tex]\( b = -3 \)[/tex].

3. Substitute the Values:
- Substitute the slope ([tex]\( m = 5 \)[/tex]) and y-intercept ([tex]\( b = -3 \)[/tex]) into the slope-intercept form equation [tex]\( y = mx + b \)[/tex].

Thus, substituting these values, we get:
[tex]\[ y = 5x - 3 \][/tex]

4. Match with Given Options:
- Option A: [tex]\( y = 5x - 3 \)[/tex]
- Option B: [tex]\( y = 5x + 3 \)[/tex]
- Option C: [tex]\( y = -3x + 5 \)[/tex]
- Option D: [tex]\( x = 3y - 5 \)[/tex]

Among these options, the equation [tex]\( y = 5x - 3 \)[/tex] matches with Option A.

5. Conclusion:
- Therefore, the correct answer is:
[tex]\[ \boxed{A} \][/tex]

Thus, the equation of the line in slope-intercept form for a line with a slope of 5 and a y-intercept at [tex]\( (0, -3) \)[/tex] is [tex]\( y = 5x - 3 \)[/tex].