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].
