Advertisements
Advertisements
प्रश्न
Line y = mx + c passes through points A(2, 1) and B(3, 2). Determine m and c.
Advertisements
उत्तर
Given, A(2, 1) and B(3, 2)
Equation of the line in two point form is
`(y - y_1)/(y_2 - y_1) = (x - x_1)/(x_2 - x_1)`
∴ The equation of the required line is
`(y - 1)/(2 - 1) = (x - 2)/(3 - 2)`
∴ `(y - 1)/1 = (x - 2)/1`
∴ y – 1 = x – 2
∴ y = x – 1
Comparing this equation with y = mx + c, we get m = 1 and c = – 1
Alternate Method:
Points A(2, 1) and B(3, 2) lie on the line y = mx + c.
∴ They must satisfy the equation.
∴ 2m + c = 1 ...(i)
and 3m + c = 2 ...(ii)
equation (ii) – equation (i) gives
m = 1
Substituting m = 1 in (i), we get
2(1) + c = 1
∴ c = 1 – 2 = – 1
APPEARS IN
संबंधित प्रश्न
Write the equation of the line :
parallel to the X−axis and at a distance of 5 unit form it and above it
Write the equation of the line :
parallel to the X-axis and at a distance of 4 unit form the point (−2, 3)
Obtain the equation of the line :
parallel to the Y−axis and making an intercept of 4 unit on the X−axis
Find the equation of the line passing through the points A(2, 0), and B(3, 4)
Find the equation of the line passing through the origin and parallel to AB, where A is (2, 4) and B is (1, 7)
Find the equation of the line containing point A(4, 3) and having inclination 120°
Find the x and y intercept of the following line:
`x/3 + y/2` = 1
Find equations of lines which contains the point A(1, 3) and the sum of whose intercepts on the coordinate axes is zero.
Find the coordinates of the orthocenter of the triangle whose vertices are A(2, −2), B(1, 1), and C(−1, 0).
Select the correct option from the given alternatives:
The equation of the line through (1, 2), which makes equal intercepts on the axes, is
Answer the following question:
Reduce the equation 6x + 3y + 8 = 0 into slope-intercept form. Hence find its slope
Answer the following question:
Find the equation of the line having slope 5 and containing point A(–1, 2).
Answer the following question:
The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6) Find equations of Perpendicular bisectors of sides
Answer the following question:
The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6) Find equations of altitudes of ∆ABC
Answer the following question:
Find the X−intercept of the line whose slope is 3 and which makes intercept 4 on the Y−axis
Answer the following question:
Two lines passing through M(2, 3) intersect each other at an angle of 45°. If slope of one line is 2, find the equation of the other line.
Answer the following question:
Find the Y-intercept of the line whose slope is 4 and which has X intercept 5
Answer the following question:
Find the equations of the diagonals of the rectangle whose sides are contained in the lines x = 8, x = 10, y = 11 and y = 12
Answer the following question:
The vertices of ∆PQR are P(2, 1), Q(−2, 3) and R(4, 5). Find the equation of the median through R.
Answer the following question:
The perpendicular from the origin to a line meets it at (−2, 9). Find the equation of the line.
Answer the following question:
P(a, b) is the mid point of a line segment between axes. Show that the equation of the line is `x/"a" + y/"b"` = 2
Answer the following question:
Show that there are two lines which pass through A(3, 4) and the sum of whose intercepts is zero.
Answer the following question:
Show that there is only one line which passes through B(5, 5) and the sum of whose intercept is zero.
If for a plane, the intercepts on the co-ordinate axes are 8, 4, 4, then the length of the perpendicular from the origin to the plane is ______
The lines `(x + 1)/(-10) = (y + 3)/-1 = (z - 4)/1` and `(x + 10)/(-1) = (y + 1)/-3 = (z - 1)/4` intersect at the point ______
The point A(b, a) lies on the straight line 2x + 3y = 13 and the point B(a, b) lies on the straight line -x + 4y = 5, then the equation of line AB is ______
The intercept of a line between the coordinate axes is divided by the point (1, 3) in the ratio 3 : 1. The equation of the line will be ______
A Plane cuts the coordinate axes X, Y, Z at A, B, C respectively such that the centroid of the Δ ABC is (6, 6, 3). Then the equation of that plane is ______.
The line L given by `x/5+y/b=1` passes through the point (13, 32). The line K is parallel to L and its equation is `x/c+y/3=1`. Then, the distance between L and K is ______.
Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 is equal to ______.
N(3, – 4) is the foot of the perpendicular drawn from the origin to a line L. Then, the equation of the line L is ______.
