(1) The equation of straight line for slope and y-intercept is .
(2) The equation of line that passes through the points and is .
(3) The constant of variation for line is .
(4) The value of is .
Further explanation:
Part (1)
Concept used:
The equation of straight line for slope and intercept can be expressed as,
....(1)
Here, is the -intercept of the straight line.
Given:
The slope of the line is and -intercept is .
Calculation:
Substitute and in the equation (1) to obtain the equation of straight line as follows,
Therefore, the equation of straight line for slope and -intercept is .
Part (2)
Concept used:
The equation of straight line that passes through the point and is expressed as,
....(2)
Here, is the slope of the line.
Now, the equation of line in the point slope form is,
Calculation:
The equation passes through the point and .
Now, substitute for , for , for and for in the equation (2) to obtain the equation of line.
Therefore, the equation in slope intercepts form for line that passes through the points and is .
Part (3)
Given:
The equation of line is .
Concept used:
If the value of varies directly with the value of that means as the value of increases, increases in the same ratio.
Here, is the constant of variation.
Calculation:
The given equation can be simplified as,
Compare the equation with the equation (3) to obtain the value of .
Therefore, the constant of variation for the given equation is .
Part (4)
Calculation:
The value of is when is . The value of varies directly with .
The constant of variation is calculated as,
The constant of variation is .
The relationship between and can be written as,
......(4)
Substitute for and for in the equation (4) to obtain the value of .
Therefore, the value of is .
Learn more:
1. A problem on line brainly.com/question/1473992
2. A problem on simplification brainly.com/question/3658196
3. A problem on permutation brainly.com/question/5199020
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: Slope, equation of line, constant of variation, y=2/3x+9, points, intercepts, straight line, slope-intercept form.