Question 12 Marks
Draw a graph of each of the following equations$: y = 3$
Answer$y = 3$
The graph of $y = 3$ is a straight line which is parallel to the $ x-$axis at a distance of $3$ units from it.
View full question & answer→Question 22 Marks
Draw a graph of each of the following equations$: x = 0$
Answer$x = 0$
The graph of $x = 0$ is the equation of the $y-$axis since the value of $'x'$ for each point $(x, y)$ on the $y-$axis is $'0'.$
View full question & answer→Question 32 Marks
Draw a graph of each of the following equations$: 2y - 5 = 0$
Answer$2 y-5=0$
$ \Rightarrow y=\frac{5}{2}$
The graph of $2 y-5=0$ is a straight line which is parallel to the $x-$axis at a distance of $\frac{5}{2}$ units from it.
View full question & answer→Question 42 Marks
Draw a graph of each of the following equations$: 2x = 7$
Answer$2 x=7$
$ \Rightarrow x=\frac{7}{2}$
The graph of $2 x=7$ is a straight line which is parallel to the $y-$axis at a distance of $\frac{7}{2}$ units from it.
View full question & answer→Question 52 Marks
Draw a graph of each of the following equations$: y - 4 = 0$
Answer$y - 4 = 0$
$\Rightarrow y = 4$
The graph of $y - 4 = 0$ is a straight line which is parallel to the $x-$axis at a distance of $4$ units from it.
View full question & answer→Question 62 Marks
Draw a graph of each of the following equations$: x + 5 = 0$
Answer$x + 5 = 0$
$\Rightarrow x = -5$
The graph of $x + 5 = 0$ is a straight line which is parallel to the $y-$axis at a distance of $5$ units from it.
View full question & answer→Question 72 Marks
Find the equation of the line, whose slope is $1$ and $y-$intercept is $0.$
AnswerEquation of a line in the slope$-$intercept form is given by$:$
$y = mx + c$
Substituting $m = 1$ and $c = 0,$ we get:
$y = (1)x + 0$
$\therefore y = x.$
View full question & answer→Question 82 Marks
Find the equation of the line, whose slope is $0$ and $y-$intercept is $-1.$
AnswerEquation of a line in the slope$-$intercept form is given by$:$
$y = mx + c$
Substituting $m = 0$ and $c = -1,$ we get:
$y = 0x + (-1)$
$∴ y = -1.$
View full question & answer→Question 92 Marks
Find the equation of the line, whose slope is $3$ and $y-$intercept is $5.$
AnswerEquation of a line in the slope-intercept form is given by$:$
$y = mx + c$
Substituting $m = 3$ and $c = 5,$ we get:
$\therefore y = 3x + 5.$
View full question & answer→Question 102 Marks
Find the slope and $y-$intercept for each of the following equations$: 6x = 7y - 12$
Answer$6x=7y-12$
$ 7y=6x+12$
$ y=\frac{6}{7} x+\frac{12}{7}$
$\therefore$ Slope $=\frac{6}{7}$ and intercept $=\frac{12}{7}$.
View full question & answer→Question 112 Marks
Find the slope and $y-$intercept for each of the following equations$: 3x - 8y + 24 = 0$
Answer$ 3 x-8 y+24=0$
$ 8 y=3 x+24$
$ y=\frac{3}{8} x+\frac{24}{8}$
$ y=\frac{3}{8} x+3$
$ \therefore$ Slope $=\frac{3}{8}$ and intercept $=3 .$
View full question & answer→Question 122 Marks
Find the inclination of the line whose slope is $\sqrt{3}$
Answer Slope $=\tan \theta$
$ \therefore \sqrt{3}=\tan \theta \ldots ($given$)$
But $\tan 60^{\circ}=\sqrt{3}$
$ \therefore \tan \theta=\tan 60^{\circ}$
$ \therefore \theta=60^{\circ} .$
View full question & answer→Question 132 Marks
Find the inclination of the line whose slope is $1$
AnswerSlope $= \tan\theta $
$\therefore 1 = \tan\theta ...($given$)$
But $ \tan 45^\circ = 1$
$\therefore \tan\theta = \tan45^\circ $
$\therefore \theta = 45^\circ .$
View full question & answer→Question 142 Marks
Find the inclination and slope of a line which is perpendicular to $y-$axis.
AnswerPerpendicular ar to $y-$axis.
Indination $= 0^\circ $
Slope
$= \tan\theta $
$= \tan0^\circ $
Slope $= 0$
View full question & answer→Question 152 Marks
Find the inclination and slope of a line which is intersecting $x-$axis at right angle.
AnswerEquidistant $x-$axis at right angle.
Indination $= 90^\circ $
Slope
$= \tan\theta $
$= \tan90^\circ $
Slope $=$ undefined
View full question & answer→Question 162 Marks
Find the inclination and slope of a line which is equidistant from the $y-$axis.
AnswerEquidistant from the $y-$axis.
Indination $= 90^\circ $
Slope
$= \tan\theta $
$= \tan90^\circ $
Slope $=$ undefined
View full question & answer→Question 172 Marks
Express the equation $3x + 5y + 15 = 0$ in the form such that$:a. x$ is subject to the formula $b. y$ is dependent variable and $x$ is independent variable.
Answer$ \text { a) } 3 x+5 y+15=0$
$ 3 x=-5 y-15$
$ x=\frac{-5 y-15}{3}$
$ x=\left(\frac{-5}{3}\right) y-5$
$ \text { b) } 3 x+5 y+15=0$
$ 5 y=-3 x-15$
$ y=\frac{-3 x-15}{5}$
$ y=\left(\frac{-3}{5}\right) x-3$
View full question & answer→Question 182 Marks
Plot the points $(-2, 3), (3, 3), (5, -2)$ and $(-5, -2)$ on a graph and join them in order. Name the figure you get.
Answer
The quadrilateral obtained is a trapezium.
View full question & answer→Question 192 Marks
Plot the points $O (0, 0), P (6, 0)$ and $R (0, 5)$ on a graph. Find the coordinates of the point $Q$ such that $\text{OPQR}$ is a rectangle.
Answer
$Q=(6,5)$ View full question & answer→Question 202 Marks
Plot the following points on the graph paper$:P(2, 5), Q(4, 0), R(0, 7), S(-3, 5), T(4, -4), U(0, -2)$ and $V(-1, -4)$
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