Question

If a line is passing through the points ( -3,4 ) and ( 2,5 ) is parallel to the line kx + 3y = 8 , then value of k is

Answer 1

Answer:

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Answer 2

The value of k is  $\frac{-3}{5}$.

Step-by-step explanation:

We are given two coordinates $(-3,4) , (2,5)$ of a line which is parallel to another line whose equation is,

$kx+3y=8$

and we have to find the value of 'k'.

• Formula used,

If two lines are parallel to each other then their slopes are also equal to each other. for example,

$m1$ and $m2$ are slopes of two lines and both lines are parallel to each other then,

$m1=m2$.

 If we are given with coordinates of line as $(x1,y1)$ and $(x2,y2).$

then their slope (m) is

$m=\frac{y2-y1}{x2-x1}$

• Calculation for m1 and m2

Let us take $m1$ for the slope of first line having coordinates and $m2$ for the slope of second line.

• slope(m1) for first line is

$(-3,4) , (2,5)$

here   $x1=-3$   ,  $y1=4$  , $x2=2$  and $y2=5$.

By using formula

$m=\frac{y2-y1}{x2-x1}$

$m1=\frac{5-4}{2-(-3)}$

$m1=\frac{1}{2+3}$

$m1=\frac{1}{5}$

Slope of first line is $\frac{1}{5}$.

• Slope (m2) for second line,

If we arrange given equation just like general equation then we easily get slope of line .

general form of equation,

$y=m*x+c$

m is for slope and c is intercept.

$kx+3y=8$

taking $kx$ to R.H.S

$3y=-kx+8$

dividing both sides by 3,

$y=\frac{-k}{3}*x+\frac{8}{3}$

by comparing it with general equation we get slope m2 as,

$m2 = \frac{-k}{3}$

Slope of first line is $\frac{-k}{3}$.

• Calculation for 'k'

for parallel lines,

$m1=m2$

so by equating both slopes we get,

$\frac{1}{5}=\frac{-k}{3}$

$k=\frac{-3}{5}$

we get the answer of this question as the value of k is $\frac{-3}{5}$.