Worksheet Chapter 9: Straight Lines

1. A straight line has an x-intercept of -6 and a y-intercept of 3. (a) Calculate its gradient. (b) Write down its equation in the form y = mx + c. (c) Determine whether the point (-4, 1) lies on this line.

2. True or False: Two straight lines are parallel if their gradients are equal (m1 = m2).

3. Find the coordinates of the point of intersection between the straight lines 2x + y = 7 and 3x - 2y = 7 using simultaneous equations.

4. The line L1 has the equation 3y = 9x - 12. Line L2 is parallel to L1 and passes through the point (2, 10). Find the equation of line L2 in the form y = mx + c.

5. Which of the following is the gradient of the line 5x - 2y = 8?

6. Line L1 passes through (1, 2) and (5, 10). Line L2 has the equation y = -x + 11. (a) Find the equation of L1. (b) Calculate the coordinates of the intersection point P between L1 and L2. (c) Line L3 is a horizontal line passing through P. Write down the equation of line L3.

7. Fill in the blank: The gradient of a straight line with x-intercept a and y-intercept b is given by m = -________.

8. True or False: The straight line y = 4 is parallel to the y-axis.

9. A straight line passes through points P(-2, 5) and Q(4, -7). Calculate: (a) The gradient of line PQ. (b) The y-intercept of line PQ.

10. In the Cartesian plane, line AB passes through A(-4, 0) and B(0, 8). Line CD is parallel to line AB and passes through point C(3, 2). (a) Find the gradient of AB. (b) Find the equation of line CD. (c) Find the x-intercept of line CD.