Question

Find k if the slope of a line passing through thevpoint (2‚4) and (5‚k) is 5/3

Answer 1

$\large\underline{\bold{Given \:Question - }}$

• Find k if the slope of a line passing through the points (2‚4) and (5‚k) is 5/3

$\large\underline{\bold{ANSWER-}}$

$\large\underline{\bold{Given- }}$

• A line passing through the points (2‚4) and (5‚k).

• Slope of line is 5/3

$\large\underline{\bold{To\:Find - }}$

• The value of k

$\large\underline{\bold{Solution-}}$

We know that,

• The slope (m) of line joining the points (a, b) and (c, d) is given by

$\rm :\longmapsto\:m \: = \dfrac{d - b}{c - a}$

So,

given that

• The slope of a line passing through the point (2‚4) and (5‚k) is 5/3

$\rm :\implies\:\dfrac{k - 4}{5 - 2} = \dfrac{5}{3}$

$\rm :\longmapsto\:\dfrac{k - 4}{3} = \dfrac{5}{3}$

$\rm :\longmapsto\:k - 4 = 5$

$\rm :\longmapsto\:k \: = \: 9$

Additional Information :-

• Slope of a line is defined as the tangent of an angle 'a' which a line makes with positive direction of x - axis, denoted by small 'm' and is given by m = tan a

• Two lines having slope m and M are parallel iff m = M

• Two lines having slope m and M are perpendicular iff Mm = - 1.

• The slope of line parallel to x - axis is 0.

• The slope of line parallel to y - axis is not defined.

• Slope of line is positive if it makes acute angle with positive direction of x axis

• Slope of line is negative if it makes obtuse angle with positive direction of x axis