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Math Chapter 8 : Test Yourself
1 / 14
Slope of two lies are $0\ $and $\infty$. What is angle between both lines?
Reasoning: A line with slope $0$ is horizontal and a line with slope $\infty$ is vertical. Horizontal and vertical lines are perpendicular, so the angle between them is $90^{o}$.
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One angle of right triangle $ABC\ $is determined by the line joining $A(1,2)\ $and $B(2,3)$. Find the third angle.
Reasoning: Slope of line joining $A(1,2)$and $B(2,3)$: $m =$ $\frac{3\ - \ 2}{2\ - \ 1} = 1$Since $tan\ \theta = 1$, the angle is $45^{o}$. The other acute angle of the right triangle is also $45^{o}$.
3 / 14
Slope of $( - 1,6)$ and $(1,y)\ $is $3$. What is $y$?
Reasoning: $m =$ $\frac{y\ - \ 6}{1\ - \ ( - \ 1)} = 3\ \ \Longrightarrow \ \ \frac{y\ - \ 6}{2} = 3\ \ \Longrightarrow \ \ y - 6 = 6\ \ \Longrightarrow \ \ y = 12$So, the correct value is $12$.
4 / 14
The line $5x - ky - 3 = 0$ passes through $(1,2)$. What is $k$?
Reasoning: Substitute $(1,2)$ in $5x - ky - 3 = 0$:$5(1) - 2k - 3 = 0\ \ \ \ \ \Longrightarrow \ \ \ \ 2 - 2k = 0\ \ \ \ \Longrightarrow \ \ \ k = 1$
5 / 14
The line $5x - 6 = 0\ \ $represents a line:
Reasoning: $5x - 6 = 0$ $\Longrightarrow$ $x =$ $\frac{6}{5}$A fixed value of '$x$' represents a vertical line, which is parallel to the $y$-axis.
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Line $y = 0\ \ $represents:
Reasoning: The equation $(y = 0)$ means all points have zero $y$-coordinate, which forms the $x$-axis.
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The line $y = b$, is above the $x$-axis, if:
Reasoning: The line $(y = b)$ lies above the $x$-axis when its $y$-coordinate is positive. Therefore, $(b > 0)$.
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The line $x = a$, is left to the $y$-axis, if:
Reasoning: The line $(x = a)$ is left of the $y$-axis when the $x$-coordinate is negative. Therefore, $(a < 0)$.
9 / 14
Slope of a line $l\ \ $is $- \ 4$. What is slope of a line perpendicular to $l\ $?
Reasoning: For perpendicular lines: $m_{1}{\ m}_{2} = - \ 1$$( - \ 4)\ m_{2} = - \ 1$ $\Longrightarrow$ $m_{2} =$ $\frac{1}{4}$So, the perpendicular slope is $\frac{1}{4}$.
10 / 14
Which of the following line has slope $\frac{2}{3}\ $?
Reasoning: Convert $(2x - 3y = 2)$ into slope form:$- \ 3y = - \ 2x + 2$ $\Longrightarrow$ $y =$ $\frac{2}{3}x - \frac{2}{3}$ $\Longrightarrow$ The slope is $\frac{2}{3}$.
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The line $y = 5x - 3\ $is written in the form:
Reasoning: The equation $(y = 5x - 3)$ is in the form $(y = mx + c)$, which is called the slope-intercept form.
12 / 14
$x$-intercept of the line $x + y = 5\ $is:
Reasoning: For $x$-intercept, put $(y = 0)$: $x + 0 = 5$ $\Longrightarrow$ $x = 5$Hence $x$-intercept is $5$.
13 / 14
A line intersects both axis at $(2,0)$ and $(0,7)$ respectively. Its $y$-intercept is:
Reasoning: The $y$-intercept is the point where the line crosses the $y$-axis. Given point is $(0,7)$, so $y$-intercept is $7$.
14 / 14
Point of intersection of lines $9x - 7y = 0$ and $8x - 11y = 0$, is:
Reasoning: Both equations have zero constant term, so when $\ x = 0\ $ and $\ y = 0$both are satisfied. Therefore, their intersection point is $(0,0)$.
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