Advertisements
Advertisements
Question
Draw the graphs of the following equations on the same system of co-ordinates. Write the co-ordinates of their points of intersection.
x + 4 = 0, y - 1 = 0, 2x + 3 = 0, 3y - 15 = 0
Advertisements
Solution
∴ x + 4 = 0
⇒ x = −4
x = −4 is the equation of the line parallel to Y-axis at a distance of 4 units from it to its left.
∴ y − 1 = 0
⇒ y = 1
y = 1 is the equation of the line parallel to X-axis at a distance of 1 unit and above the X-axis.
∴ 2x + 3 = 0
⇒ x = `-3/2`
`x = - 3/2` is the equation of the line parallel to Y-axis at a distance of `3/2` units from it to its left.
∴ 3y − 15 = 0
⇒ y = `15/3`
⇒ y = 5
y = 5 is the equation of the line parallel to X-axis at a distance of 5 units and above the X-axis.
It can be seen from the figure that the co-ordinates of the points of intersection are `(-3/2 , 1), (-3/2 , 5),(-4,5) "and" (-4,1)`.
APPEARS IN
RELATED QUESTIONS
Draw the graph of the equation given below.
x + y = 2
The following table gives production yield in kg per hectare of wheat of 100 farms of a village:
| Production yield (kg/hectare): |
40 – 45 | 45 – 50 | 50 – 55 | 55 – 60 | 60 – 65 | 65 – 70 |
| Number of farms | 4 | 6 | 16 | 20 | 30 | 24 |
Change the distribution to 'a more than' type distribution, and draw its ogive.
Draw the graph for the linear equation given below:
x = 3
Draw the graph for the linear equation given below:
x = 0
Draw the graph for the linear equation given below:
4x - y = 0
Draw the graph for the linear equation given below:
3x + 2y = 0
Draw the graph for the linear equation given below:
y = 2x + 3
Draw the graph for the linear equation given below:
y = `(2x)/(3) - 1`
Draw the graph for the linear equation given below:
y = `4x - (5)/(2)`
Draw the graph for the equation given below:
2x - 5y = 10
For the linear equation, given above, draw the graph and then use the graph drawn (in the following case) to find the area of a triangle enclosed by the graph and the co-ordinates axes:
7 - 3 (1 - y) = -5 + 2x
For the pair of linear equations given below, draw graphs and then state, whether the lines drawn are parallel or perpendicular to each other.
y = x - 3
y = - x + 5
Draw the graph of equation 3x – 4y = 12. Use the graph drawn to find:
- y1, the value of y, when x = 4.
- y2, the value of y, when x = 0.
Draw the graph of equation `x/(4) + y/(5) = 1` Use the graph drawn to find:
(i) x1, the value of x, when y = 10
(ii) y1, the value of y, when x = 8.
Use the graphical method to show that the straight lines given by the equations x + y = 2, x - 2y = 5 and `x/(3) + y = 0` pass through the same point.
Draw a graph of each of the following equations: 3y + 2x = 11
Draw a graph of each of the following equations: y = `(3)/(5) x - 1`
Draw a graph of the equation 3x - y = 7. From the graph find the value of:
(i) y, when x = 1
(ii) x, when y = 8
