Mathematics: What is the x-intercept of the line with this equation -2x + 1/3y =18 0)plz answer fast and explain if you can

What is the x-intercept of the line with this

Ответ:

thegurl41

16.12.2020

Mathematics

The correct options are

(1) (B) parallel

(2) (C) neither.

Step-by-step explanation: We know that two straight lines are

(i) parallel, if they have equal slopes,

(ii) perpendicular, if the product of their slopes is -1.

Also, the slope-intercept form of the equation of a straight line is

y=mx+c, where m is the slope.

(1) We are given to check whether the following lines are parallel, perpendicular or neither :

$y=-2x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5x+10y=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Comparing equation (i) with the slope-intercept form, we get

m_1=-2.

From equation (ii), we have

$-5x+10y=5\\\\\Rightarrow -x+2y=1\\\\\Rightarrow 2y=x+1\\\\\Rightarrow y=\dfrac{1}{2}x+\dfrac{1}{2}.$

So, $m_2=\dfrac{1}{2}.$

We have

$m_1\times m_2=(-2)\times\dfrac{1}{2}=-1.$

Therefore, the given lines are perpendicular.

Option (B) is CORRECT.

(2) We are given to check whether the following lines are parallel, perpendicular or neither :

$y=-\dfrac{1}{5}x+6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)\\\\-2x+10y=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$