Mathematics
Draw the graph of the straight line whose table is given below.
| x | -1 | 1 | .... | 0 | 3 |
| y | -3 | .... | -7 | -1 | 5 |
(i) Write down the linear relation between x and y.
(ii) Use the graph to find the missing numbers.
Graphical Solution
2 Likes
Answer
Plot the given points (-1, -3), (0, -1) and (3, 5) on a graph paper.
Draw a straight line passing through these points.
(i) Let the linear relation between the variable x and y be y = mx + c.
Since, the graph passes through the point (-1, -3); substitute x = -1 and y = -3 in y = mx + c.
This gives -3 = -1m + c ……………(1)
Again, the graph passes through the point (0, -1); substitute x = 0 and y = -1 in y = mx + c
This gives -1 = 0m + c
⇒ c = -1 ……………(2)
Substituting the value of c in (1),
⇒ -3 = -1m + (-1)
⇒ -m = -3 + 1
⇒ -m = -2
⇒ m = 2
∴ Required relation is : y = mx + c i.e. y = 2x - 1
Hence, the equation y = 2x - 1.
(ii) Through x = 1, draw a vertical line which meets the graph at a point, say A. Through A, draw a horizontal line which meets the y-axis at y = 1.
∴ when x = 1, y = 1.
Through y = -7, draw a horizontal line which meets the graph at a point, say B. Through B, draw a vertical line which meets the x-axis at x = -3.
∴ when y = -7, x = -3.
Hence, the points are (1, 1) and (-3, -7).
Answered By
1 Like
Related Questions
Draw the graph of straight line y = -2x + 3. Use your graph to find :
(i) the intercept on y-axis
(ii) the area between the line and co-ordinate axes.
Find graphically the vertices of the triangle whose sides have the equations 2y - x = 8, 5y - x = 14 and y - 2x = 1. Take 1 cm = 1 unit on both the axes.
On the same graph paper, draw the straight lines represented by equations:
x = 5, x + 5 = 0, y + 3 = 0 and y = 3.
Also, find the area and perimeter of the rectangle formed by the intersection of these lines.
On a graph paper, mark the points A(-1, -1) and B(2, 5). Draw a straight line passing through A and B. If points (m, 4) and (0.5, n) lie on this line, use graphical method of finding the values of m and n.