Class 11 Maths Chapter 9 Straight Lines – Exercise 9.1 NCERT Solutions

Introduction

Exercise 9.1 introduces the concept of straight lines in coordinate geometry. You will learn slope, intercepts, and different forms of equations of a line. This exercise builds the foundation for analytical geometry and higher‑level mathematics.

Key Concepts

1. Slope of Line:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

2. Equation of Line (Point‑Slope Form):

$$y-y_1=m(x-x_1)$$

3. Slope‑Intercept Form:

$$y=mx+c$$

4. Two‑Point Form:

$$\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$$

5. Intercept Form:

$$\frac{x}{a}+\frac{y}{b}=1$$

NCERT Questions with Solutions (10)

Q1. Find slope of line passing through points (2,3) and (4,7).

$$m=\frac{7-3}{4-2}=\frac{4}{2}=2$$

Q2. Find slope of line passing through points (1,2) and (3,8).

$$m=\frac{8-2}{3-1}=\frac{6}{2}=3$$

Q3. Find slope of line passing through points (-1,4) and (2,-2).

$$m=\frac{-2-4}{2-(-1)}=\frac{-6}{3}=-2$$

Q4. Find equation of line passing through (1,2) with slope 3.

$$y-2=3(x-1)⟹y=3x-1$$

Q5. Find equation of line passing through (0,4) with slope 2.

$$y-4=2(x-0)⟹y=2x+4$$

Q6. Find equation of line passing through (2,3) and (4,7). Slope $m=2$.

$$y-3=2(x-2)⟹y=2x-1$$

Q7. Find equation of line passing through (1,-1) and (2,1). Slope $m=\frac{1-(-1)}{2-1}=2$.

$$y+1=2(x-1)⟹y=2x-3$$

Q8. Find equation of line with x‑intercept 3 and y‑intercept 4.

$$\frac{x}{3}+\frac{y}{4}=1$$

Q9. Find equation of line passing through (0,0) with slope $\frac{1}{2}$.

$$y=\frac{1}{2}x$$

Q10. Find equation of line passing through (2,5) parallel to line $y=3x+1$. Slope $m=3$.

$$y-5=3(x-2)⟹y=3x-1$$

FAQs (10)

1. What is slope of line? Ratio of change in $y$ to change in $x$.

2. What is slope‑intercept form? $y=mx+c$.

3. What is point‑slope form? $y-y_1=m(x-x_1)$.

4. What is two‑point form? Equation using two given points.

5. What is intercept form? $\frac{x}{a}+\frac{y}{b}=1$.

6. What is x‑intercept? Point where line cuts x‑axis.

7. What is y‑intercept? Point where line cuts y‑axis.

8. What is slope of vertical line? Undefined.

9. What is slope of horizontal line? Zero.

10. Why is this exercise important? It builds foundation for coordinate geometry and analytical problem solving.

Conclusion

Exercise 9.1 has 10 solved questions and 10 FAQs that strengthen your understanding of straight lines, slope, and different forms of equations. This builds the foundation for advanced coordinate geometry in Class 11 Maths.

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New Syllabus-Class 11 Maths Chapter 9 Straight Lines – Exercise 9.1 NCERT Solutions