Question

Which of the following statements are true

(a) If a line is parallel to the y axis its slope is not defined

(b) If the slope of a line is -1, its inclination is 45 degrees

(c) If a line passes through (0,4) and (-6,2) , its slope is -1

(d) The slope of the line x=y is 1

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Answer 1

AnswEr :

Generally, slope is given as :

$\boxed{\boxed{\sf m = \dfrac{y_2 - y_1}{x_2 - x_1}}}$

When a line is parallel to y - axis, the x coordinates become zero.

$\implies \sf \: m = \dfrac{y_2 - y_1}{0} \\ \\ \implies \sf \: m = \infty - - - - - - (a)$

Slope is defined as the tangent of the angle made by the straight line.

$\sf \: m = tan(45) \neq - 1$

When a line passes through (0,4) and (-6,2),

$\implies \sf \: m = \dfrac{2 - 4}{ - 6 - 0} \\ \\ \implies \sf \: m = \dfrac{1}{3} \neq1$

Given line is x - y = 0

$\sf \: m = - \dfrac{coefficint \: of \: x}{coefficient \: of \: y} \\ \\ \implies \sf \: m = - ( - \dfrac{1}{ 1} ) = 1--------(d)$

First and Fourth statements are true.

Answer 2

Generally, slope is given as :

\boxed{\boxed{\sf m = \dfrac{y_2 - y_1}{x_2 - x_1}}}

m=

x

2

−x

1

y

2

−y

1

When a line is parallel to y - axis, the x coordinates become zero.

\begin{gathered}\implies \sf \: m = \dfrac{y_2 - y_1}{0} \\ \\ \implies \sf \: m = \infty - - - - - - (a)\end{gathered}

⟹m=

0

y

2

−y

1

⟹m=∞−−−−−−(a)

Slope is defined as the tangent of the angle made by the straight line.

\sf \: m = tan(45) \neq - 1m=tan(45)



=−1

When a line passes through (0,4) and (-6,2),

\begin{gathered}\implies \sf \: m = \dfrac{2 - 4}{ - 6 - 0} \\ \\ \implies \sf \: m = \dfrac{1}{3} \neq1\end{gathered}

⟹m=

−6−0

2−4

⟹m=

3

1



=1

Given line is x - y = 0

\begin{gathered}\sf \: m = - \dfrac{coefficint \: of \: x}{coefficient \: of \: y} \\ \\ \implies \sf \: m = - ( - \dfrac{1}{ 1} ) = 1--------(d)\end{gathered}

m=−

coefficientofy

coefficintofx

⟹m=−(−

1

1

)=1−−−−−−−−(d)

First and Fourth statements are true....