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Sagot :
Given:
A line is perpendicular to the line [tex]y=\dfrac{7}{2}x-13[/tex].
The line passes through the x-axis at 21.
To find:
The equation of the line in slope intercept form.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex]
Where, m is the slope and b is the y-intercept.
The given line is:
[tex]y=\dfrac{7}{2}x-13[/tex]
So, the slope of this line is [tex]\dfrac{7}{2}[/tex].
The product of slopes of two perpendicular lines is -1.
Let m be the slope of required line. Then the slope of the required line is:
[tex]m\times \dfrac{7}{2}=-1[/tex]
[tex]m=-\dfrac{2}{7}[/tex]
The line passes through the x-axis at 21. It means the line passes through the point (21,0). So, the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-0=-\dfrac{2}{7}(x-21)[/tex]
[tex]y=-\dfrac{2}{7}(x)-\dfrac{2}{7}(-21)[/tex]
[tex]y=-\dfrac{2}{7}x+6[/tex]
Therefore, the equation of the required line is [tex]y=-\dfrac{2}{7}x+6[/tex].
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