Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
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].
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].
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.