## 1. The general form of a linear equation in two variables is:

### Answer:

### Explanation:

A linear equation in two variables is represented as ax + by + c = 0 where a and b are not simultaneously zero.

## 2. For the equation 2x + 3y = 6, x-intercept is:

### Answer:

### Explanation:

For the x-intercept, y = 0. Plugging this into the equation gives x = 3.

## 3. For the equation 3x – 4y = 12, y-intercept is:

### Answer:

### Explanation:

For the y-intercept, x = 0. Substituting this value gives y = -3.

## 4. A solution of the equation 2x + y = 7 is:

### Answer:

### Explanation:

Substituting x=0, we get y=7.

## 5. How many solutions does a linear equation in two variables have?

### Answer:

### Explanation:

A linear equation in two variables represents a straight line, and every point on the line is a solution.

## 6. The graph of 3x + y = 5 will be a:

### Answer:

### Explanation:

Equations in two variables of degree 1 always represent a straight line.

## 7. If a line intersects x-axis at (a, 0) and y-axis at (0, b), then its equation is:

### Answer:

### Explanation:

Using the intercept form of a line.

## 8. Which of the following is NOT a linear equation in two variables?

### Answer:

### Explanation:

The equation has a term of degree 2.

## 9. If (2, 3) is a solution of the linear equation in two variables ax + by = c, then:

### Answer:

### Explanation:

By substituting the given values of x and y.

## 10. Two parallel lines have:

### Answer:

### Explanation:

Parallel lines have equal slopes but different y-intercepts.

## 11. The graph of x = 3 is:

### Answer:

### Explanation:

x=3 represents a vertical line at x=3 on the graph.

## 12. The equation of a line passing through the origin is of the form:

### Answer:

### Explanation:

Lines passing through the origin have the form y = mx where m is the slope.

## 13. If two lines are perpendicular, the product of their slopes is:

### Answer:

### Explanation:

The product of the slopes of two perpendicular lines is always -1.

## 14. The equation representing a line parallel to x-axis and at a distance of 4 units below it is:

### Answer:

### Explanation:

This line will be parallel to the x-axis and will pass through y=-4.

## 15. A line with zero slope is:

### Answer:

### Explanation:

A horizontal line has a slope of 0.

## 16. The slope of the line 2x – 3y = 6 is:

### Answer:

### Explanation:

Rearranging the equation to the form y = mx + c, we get the slope m = 3/2.

## 17. Which of the following equations represents a line with undefined slope?

### Answer:

### Explanation:

The equation x=5 represents a vertical line, which has an undefined slope.

## 18. The slope of the line passing through the points (1,2) and (3,6) is:

### Answer:

### Explanation:

Using the slope formula, (y2-y1)/(x2-x1) = (6-2)/(3-1) = 2.

## 19. For the equation y = mx, the y-intercept is:

### Answer:

### Explanation:

The line passes through the origin, so y-intercept is 0.

## 20. Which of the following is the equation of the y-axis?

### Answer:

### Explanation:

All points on the y-axis have x-coordinate as 0.