The concept of straight lines in mathematics is not just about connecting two points. It delves deeper into understanding the relationship between various points, slopes, intercepts, and even equations that define these lines. Whether it’s to determine the slope between two points or to find the equation of a line given certain parameters, this topic provides foundational knowledge for higher-level geometrical concepts. Ready to challenge yourself? Here are 20 multiple-choice questions on Straight Lines to test your knowledge.

## 1. What is the slope of the line passing through the points (2,3) and (4,7)?

### Answer:

### Explanation:

Slope = (y2-y1)/(x2-x1) = (7-3)/(4-2) = 2.

## 2. The equation of the x-axis is:

### Answer:

### Explanation:

The x-axis has all points where y-coordinate is 0.

## 3. If a line has a slope of -3 and a y-intercept of 4, its equation is:

### Answer:

### Explanation:

Using y = mx + c where m is the slope and c is the y-intercept.

## 4. Two lines with slopes m1 and m2 are perpendicular if:

### Answer:

### Explanation:

Two lines are perpendicular if the product of their slopes is -1.

## 5. The distance between the points (1,2) and (4,6) is:

### Answer:

### Explanation:

Using the distance formula, we get √[(4-1)^2 + (6-2)^2] = √13.

## 6. Which of the following points lies on the line y = 2x + 1?

### Answer:

### Explanation:

Plugging x=1 in the equation, we get y = 3.

## 7. The equation representing a line parallel to the x-axis and passing through (3,4) is:

### Answer:

### Explanation:

A line parallel to the x-axis has the same y-coordinate throughout.

## 8. The midpoint of the segment joining (1,2) and (3,4) is:

### Answer:

### Explanation:

Using the midpoint formula, we get [(1+3)/2, (2+4)/2] = (2,3).

## 9. The slope of a line making an angle of 45° with the positive direction of x-axis is:

### Answer:

### Explanation:

Tan(45°) = 1, which is the slope of the line.

## 10. The equation of the line passing through the point (2,3) and parallel to y = x is:

### Answer:

### Explanation:

Parallel lines have the same slope. So, it will have the slope 1. Using point-slope form, we get y – 3 = 1(x – 2).

## 11. The y-intercept of the line 3x – 2y = 6 is:

### Answer:

### Explanation:

Set x=0 in the equation to get y-intercept.

## 12. If two lines are parallel, their slopes are:

### Answer:

### Explanation:

Parallel lines have the same slope.

## 13. A line with undefined slope is:

### Answer:

### Explanation:

Vertical lines have no run, hence the slope is undefined.

## 14. The slope of the line perpendicular to 3x + 4y = 12 is:

### Answer:

### Explanation:

The slope of the given line is -3/4. The negative reciprocal is -4/3.

## 15. The equation of a line with zero slope passing through (2,5) is:

### Answer:

### Explanation:

A line with zero slope is horizontal, and all its points have the same y-coordinate.

## 16. Which of the following represents a line?

### Answer:

### Explanation:

Only this option is a linear equation.

## 17. For what values of k will the lines 3x – ky = 6 and 6x – 2ky = 12 be parallel?

### Answer:

### Explanation:

For the lines to be parallel, the ratios of coefficients of x and y should be equal. This gives k ≠ 2.

## 18. If the points (1,2), (3, k), and (5,8) are collinear, the value of k is:

### Answer:

### Explanation:

For collinearity, slopes between any two pairs of these points should be the same. This gives k=5.

## 19. The general form of the equation of a line is:

### Answer:

### Explanation:

This represents a linear equation in two variables.

## 20. If the coordinates of two ends of a line segment are (1,2) and (3,4), the length of the segment is:

### Answer:

### Explanation:

Using the distance formula, the length is 2√2.