Respuesta :
Given:
Consider the given equation is
[tex]y=\dfrac{2}{5}x-1[/tex]
To find:
The equation of a line that is perpendicular to the graph of given line.
Solution:
Slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
Equation of given line is
[tex]y=\dfrac{2}{5}x-1[/tex]
Here, slope is [tex]\dfrac{2}{5}[/tex].
We know that, product of slopes of two perpendicular lines is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]\dfrac{2}{5}\times m_2=-1[/tex]
[tex]m_2=-\dfrac{5}{2}[/tex]
The slope of perpendicular line is [tex]-\dfrac{5}{2}[/tex].
Only in option C, the slope of the line is [tex]-\dfrac{5}{2}[/tex].
Therefore, the correct option is C.
From the given option the slope of the line -5/2 is shown by the equation [tex]y=-\dfrac{5}{2}x-4[/tex] that is option B) and this can be determined by using the slope-intercept form.
Given :
Equation -- [tex]y=\dfrac{2}{5}x-1[/tex] ---- (1)
First, determine the slope of the given line by using the slope-intercept form. The slope-intercept is given by the equation:
y = mx + c
Now, compare equation (1) with the above equation.
[tex]\rm m_1 =\dfrac{2}{5}[/tex]
c = -1
For a line to be perpendicular to the other line the product of the slope of both the line is equal to -1, that is:
[tex]\rm m_1m_2 = -1[/tex]
So, the slope of the line perpendicular to the line [tex]y=\dfrac{2}{5}x-1[/tex] is:
[tex]\rm m_2 = -\dfrac{5}{2}[/tex]
So, from the given option the slope of the line -5/2 is shown by the equation [tex]y=-\dfrac{5}{2}x-4[/tex] that is option B).
For more information, refer to the link given below:
https://brainly.com/question/18666670
