Gradient of linear graphs：練習問題

A straight line passes through the points \(A(3, 2)\) and \(B(9, 6)\).
Determine the gradient of this line.

Find the gradient of the straight line that passes through the points \(A(-5, 2)\) and \(B(1, -10)\).

A straight line passes through point \(P(k, 2k)\) and point \(Q(5, 11)\).
Given that the gradient of the line is \(3\), find the value of \(k\).

A straight line is plotted on a coordinate grid. For every 1 unit the line moves to the right horizontally, it moves 3 units upwards vertically. Determine the gradient of this line.

The line passing through \(P(k, 4)\) and \(Q(5, 10)\) has a gradient of \(2\).
Find the value of \(k\).

Determine the gradient of the straight line that passes through the points with coordinates \((0, 8)\) and \((4, 0)\).

Determine the gradient of the straight line that passes through the coordinates \(A(-4, -2)\) and \(B(2, 10)\).

Calculate the gradient of a line that is perpendicular to the line with equation \(3x + 4y = 12\).

A straight line is drawn on a coordinate grid. The line passes through the points A \((1, 2)\) and B \((4, 8)\).

(a) Find the gradient of the line passing through points A and B.

(b) Find the coordinates of the midpoint of the line segment AB.

Consider the points A(-2, 5), B(4, 1), and C(7, y) in a Cartesian coordinate system.

(a) Calculate the gradient of the line segment AB.

(b) Find the equation of the line passing through A and B. Give your answer in the form $$y = mx + c$$.

(c) The line segment BC is parallel to the line $$2x + 3y = 10$$. Find the value of y.