Class 10 Equation of a Straight Line Mock Test (ICSE)

Topics in Equation of a Straight Line

• Slope and inclination of a line
• Slope from two points
• Slope-intercept form
• Point-slope form
• Parallel and perpendicular lines

Equation of a Straight Line practice questions with answers

1. Q1Multiple choice·1 mark
   The slope of the line passing through the origin and the midpoint of the line segment joining the points $(3, -4)$ and $(5, 2)$ is:

   1. (a)$-4$
   2. (b)$-\frac{1}{4}$
   3. (c)$4$
   4. (d)$\frac{1}{4}$
   Show answer and step marks

   1. Correct option: (b) $-\frac{1}{4}$. The midpoint of the line segment joining $(3, -4)$ and $(5, 2)$ is $\left(\frac{3+5}{2}, \frac{-4+2}{2}\right) = (4, -1)$. The slope of the line joining $(0, 0)$ and $(4, -1)$ is $\frac{-1 - 0}{4 - 0} = -\frac{1}{4}$.+1

   Answer: (b)
2. Q2Multiple choice·1 mark
   The inclination of a line whose slope is $-\frac{1}{\sqrt{3}}$ is:

   1. (a)$60^\circ$
   2. (b)$150^\circ$
   3. (c)$30^\circ$
   4. (d)$120^\circ$
   Show answer and step marks

   1. Correct option: (b) $150^\circ$. The slope $m$ is given by $m = \tan \theta$, so $\tan \theta = -\frac{1}{\sqrt{3}}$. Since $\tan(180^\circ - 30^\circ) = -\frac{1}{\sqrt{3}}$, the inclination $\theta = 150^\circ$.+1

   Answer: (b)
3. Q3Multiple choice·1 mark
   The y-intercept of the line $2x - 3y + 6 = 0$ is:

   1. (a)$3$
   2. (b)$-\frac{2}{3}$
   3. (c)$2$
   4. (d)$-2$
   Show answer and step marks

   1. Correct option: (c) $2$. Rewriting the equation $2x - 3y + 6 = 0$ in slope-intercept form $y = mx + c$: $3y = 2x + 6 \implies y = \frac{2}{3}x + 2$. The y-intercept is $2$.+1

   Answer: (c)
4. Q4Multiple choice·1 mark
   If the line passing through the points $(2, 5)$ and $(x, 3)$ is perpendicular to the line whose slope is $\frac{1}{2}$, then the value of $x$ is:

   1. (a)$1$
   2. (b)$3$
   3. (c)$5$
   4. (d)$-3$
   Show answer and step marks

   1. Correct option: (b) $3$. The slope of the line passing through $(2, 5)$ and $(x, 3)$ is $\frac{3 - 5}{x - 2} = \frac{-2}{x - 2}$. Since the lines are perpendicular, the product of their slopes is $-1$: $\left(\frac{-2}{x - 2}\right) \times \frac{1}{2} = -1$, which gives $x - 2 = 1$, so $x = 3$.+1

   Answer: (b)

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