Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Certainly! Let's address each part of the question step-by-step.
### Part (a):
You need to find the equation of a straight line with a given gradient (slope) and y-intercept.
1. Gradient (Slope): The gradient is given as [tex]\(3\)[/tex].
2. Y-intercept: The y-intercept is given as [tex]\(-4\)[/tex].
The general form of the equation of a straight line is:
[tex]\[ y = mx + c \][/tex]
where:
- [tex]\(m\)[/tex] is the gradient
- [tex]\(c\)[/tex] is the y-intercept
Plugging in the given values, we get:
[tex]\[ y = 3x + (-4) \][/tex]
So, the equation of the line for part (a) is:
[tex]\[ y = 3x - 4 \][/tex]
### Part (b):
You need to find the equation of a straight line with a given angle of inclination and y-intercept.
1. Angle of Inclination: The angle of inclination is given as [tex]\(135^\circ\)[/tex].
2. Y-intercept: The y-intercept is given as [tex]\(5\)[/tex].
The gradient of a line can be found using the tangent of the angle of inclination:
[tex]\[ m = \tan(\theta) \][/tex]
where:
- [tex]\(\theta\)[/tex] is the angle of inclination.
For [tex]\(\theta = 135^\circ\)[/tex]:
[tex]\[ m = \tan(135^\circ) \][/tex]
The value of [tex]\(\tan(135^\circ)\)[/tex] is [tex]\(-1.0000000000000002\)[/tex] (which is approximately [tex]\(-1\)[/tex]).
The general form of the equation of a straight line is:
[tex]\[ y = mx + c \][/tex]
Plugging in the calculated gradient and the given y-intercept, we get:
[tex]\[ y = -1.0000000000000002x + 5 \][/tex]
So, the equation of the line for part (b) is:
[tex]\[ y = -1.0000000000000002x + 5 \][/tex]
To summarize:
- The equation of the line with a gradient of 3 and a y-intercept of -4 is:
[tex]\[ y = 3x - 4 \][/tex]
- The equation of the line with an angle of inclination of 135° and a y-intercept of 5 is:
[tex]\[ y = -1.0000000000000002x + 5 \][/tex]
### Part (a):
You need to find the equation of a straight line with a given gradient (slope) and y-intercept.
1. Gradient (Slope): The gradient is given as [tex]\(3\)[/tex].
2. Y-intercept: The y-intercept is given as [tex]\(-4\)[/tex].
The general form of the equation of a straight line is:
[tex]\[ y = mx + c \][/tex]
where:
- [tex]\(m\)[/tex] is the gradient
- [tex]\(c\)[/tex] is the y-intercept
Plugging in the given values, we get:
[tex]\[ y = 3x + (-4) \][/tex]
So, the equation of the line for part (a) is:
[tex]\[ y = 3x - 4 \][/tex]
### Part (b):
You need to find the equation of a straight line with a given angle of inclination and y-intercept.
1. Angle of Inclination: The angle of inclination is given as [tex]\(135^\circ\)[/tex].
2. Y-intercept: The y-intercept is given as [tex]\(5\)[/tex].
The gradient of a line can be found using the tangent of the angle of inclination:
[tex]\[ m = \tan(\theta) \][/tex]
where:
- [tex]\(\theta\)[/tex] is the angle of inclination.
For [tex]\(\theta = 135^\circ\)[/tex]:
[tex]\[ m = \tan(135^\circ) \][/tex]
The value of [tex]\(\tan(135^\circ)\)[/tex] is [tex]\(-1.0000000000000002\)[/tex] (which is approximately [tex]\(-1\)[/tex]).
The general form of the equation of a straight line is:
[tex]\[ y = mx + c \][/tex]
Plugging in the calculated gradient and the given y-intercept, we get:
[tex]\[ y = -1.0000000000000002x + 5 \][/tex]
So, the equation of the line for part (b) is:
[tex]\[ y = -1.0000000000000002x + 5 \][/tex]
To summarize:
- The equation of the line with a gradient of 3 and a y-intercept of -4 is:
[tex]\[ y = 3x - 4 \][/tex]
- The equation of the line with an angle of inclination of 135° and a y-intercept of 5 is:
[tex]\[ y = -1.0000000000000002x + 5 \][/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.