Find the gradient and the equation of the line passing through the points:
(i) A(–2, 1) and B(3, –4)
(ii) A(4, –2) and B(2, –3)

Question

Find the gradient and the equation of the line passing through the points: (i) A(–2, 1) and B(3, –4) (ii) A(4, –2) and B(2, –3)

KnowledgeBoat · Accepted Answer

(i) Slope of AB = = = = -1. Equation : y - y1 = m(x - x1) ⇒ y - 1 = -1(x - (-2)) ⇒ y - 1 = -1(x + 2) ⇒ y - 1 = -x - 2 ⇒ x + y - 1 + 2 = 0 ⇒ x + y + 1 = 0. Hence, slope = -1, equation of AB is x + y + 1 = 0. (ii) Slope of AB = = = = . Equation : y - y1 = m(x - x1) ⇒ y - (-2) = (x - 4) ⇒ 2(y + 2) = (x - 4) ⇒ 2y + 4 = x - 4 ⇒ x - 2y - 4 - 4 = 0 ⇒ x - 2y - 8 = 0. Hence, slope = , equation of AB is x - 2y - 8 = 0.

Mathematics

Find the gradient and the equation of the line passing through the points:
(i) A(–2, 1) and B(3, –4)
(ii) A(4, –2) and B(2, –3)

Straight Line Eq

Related Questions

Find the equation of a line:
(i) Whose slope is 4 and which passes through the point (3, 7)
(ii) Whose slope is –3 and which passes through the point (–2, 3)

A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects x-axis and y-axis at the points A and B respectively and M is the mid-point of AB. Find :
(i) the equation of the line
(ii) the co-ordinates of A and B
(iii) the co-ordinates of M

A(2, 3) and B(–2, 5) are two given points. Find :
(i) the gradient of AB
(ii) the equation of AB
(iii) the co-ordinates of the point, where AB intersects x-axis.

Mathematics

Find the gradient and the equation of the line passing through the points:(i) A(–2, 1) and B(3, –4)(ii) A(4, –2) and B(2, –3)

Straight Line Eq

Related Questions

Find the equation of a line:(i) Whose slope is 4 and which passes through the point (3, 7)(ii) Whose slope is –3 and which passes through the point (–2, 3)

A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects x-axis and y-axis at the points A and B respectively and M is the mid-point of AB. Find :(i) the equation of the line(ii) the co-ordinates of A and B(iii) the co-ordinates of M

A(2, 3) and B(–2, 5) are two given points. Find :(i) the gradient of AB(ii) the equation of AB(iii) the co-ordinates of the point, where AB intersects x-axis.

Find the gradient and the equation of the line passing through the points:
(i) A(–2, 1) and B(3, –4)
(ii) A(4, –2) and B(2, –3)

Find the equation of a line:
(i) Whose slope is 4 and which passes through the point (3, 7)
(ii) Whose slope is –3 and which passes through the point (–2, 3)

A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects x-axis and y-axis at the points A and B respectively and M is the mid-point of AB. Find :
(i) the equation of the line
(ii) the co-ordinates of A and B
(iii) the co-ordinates of M

A(2, 3) and B(–2, 5) are two given points. Find :
(i) the gradient of AB
(ii) the equation of AB
(iii) the co-ordinates of the point, where AB intersects x-axis.