Straight Lines quiz

The slope of the x-axis is:

The slope of the line 2x - 3y + 6 = 0 is:

The intercepts of x/4 - y/3 = 1 on the x- and y-axes are:

The lines y = 2x + 3 and y = 2x - 5 are:

A line with inclination 135 degrees has slope:

The distance of the origin from 3x + 4y = 10 is:

The line through the origin with slope 3 is:

If two lines are perpendicular and one has slope 2, the other has slope:

The slope of a vertical line is:

The y-intercept of y = 4x - 7 is:

Find the equation of the line with slope 1/2 and y-intercept -3. (2 marks)

Find the equation of the line with intercepts 3 and 2 on the axes. (2 marks)

Find the distance of (3, -5) from 3x - 4y - 26 = 0. (2 marks)

Find the area of the triangle with vertices (4, 4), (3, 5) and (-1, -1). (2 marks)

Find the angle between the x-axis and the line through (3, -1) and (4, -2). (2 marks)

Write the equation of the y-axis and of the line parallel to it through (-4, 1). (2 marks)

Find the slope of the line making intercepts -3 and 4 on the axes. (2 marks)

Show that the line through (4, 5) and (6, 9) is parallel to the line through (1, 2) and (3, 6). (2 marks)

Reduce 3x - 4y + 12 = 0 to the intercept form. (2 marks)

Find the value of k if the line kx + 2y = 5 is perpendicular to 2x - y = 3. (2 marks)

Find the distance of (-1, 1) from the line 12(x + 6) = 5(y - 2). (3 marks)

Find the equation of the line through (2, 2) that cuts off intercepts on the axes whose sum is 9. (3 marks)

Find the equation of the line through (0, 2) making an angle of 2pi/3 with the positive x-axis. (3 marks)

Find the angle between the lines sqrt(3)x + y = 1 and x + sqrt(3)y = 1. (3 marks)

Find the point on the x-axis that is equidistant from (7, 6) and (3, 4). (3 marks)

Read the passage and answer the questions. A taxi company charges fares according to y = 12x + 50, where x is the distance in km and y the fare in rupees. (i) What is the slope and what does it mean? (ii) What is the y-intercept and what does it mean? (iii) Find the fare for 8 km. (5 marks)

Read the passage and answer the questions. The Fahrenheit and Celsius scales are related linearly. Water freezes at 0 C or 32 F and boils at 100 C or 212 F. (i) Find the slope of the line through (0, 32) and (100, 212). (ii) Write F in terms of C. (iii) Find F when C = 37. (5 marks)

Read the passage and answer the questions. A wheelchair ramp rises 1 m over a horizontal distance of 12 m. (i) Find the slope of the ramp. (ii) Write the equation of the ramp line if it starts at the origin. (iii) Find the height of the ramp at a horizontal distance of 6 m. (5 marks)

Read the passage and answer the questions. A straight road passes through the points (2, 3) and (6, 11) on a town map. A house stands at (1, 8). (i) Find the slope of the road. (ii) Find the equation of the road. (iii) Find the shortest distance of the house from the road. (5 marks)

Read the passage and answer the questions. A milk vendor sells 980 litres a week at Rs 14 per litre and 1220 litres a week at Rs 16 per litre. Assume a linear relation between price and demand. (i) Find the slope of the line through (14, 980) and (16, 1220). (ii) Write the equation of the line. (iii) Estimate the weekly sale at Rs 17 per litre. (5 marks)

Define the slope of a line. Derive the conditions for two lines to be parallel and perpendicular, and explain the collinearity test. (6 marks)

Derive the formula for the acute angle between two lines with slopes m1 and m2. Find the angle between lines with slopes 1/2 and 3. (6 marks)

Derive the formula for the perpendicular distance of a point (x1, y1) from the line Ax + By + C = 0. (6 marks)

Explain the slope-intercept form and the intercept form of a line. Reduce 3x - 4y + 12 = 0 to both forms and find its slope and intercepts. (6 marks)

Find the equations of the lines through (3, 2) that make an angle of 45 degrees with the line x - 2y = 3. (6 marks)