Answer:
[tex]y = \frac{3}{5} x + \frac{13}{5} [/tex]
Step-by-step explanation:
The equation of a line can be written in the slope-intercept form y= mx +c, where m is the slope and c is the y-intercept.
Let's rewrite the given equation into the slope-intercept form, so that we can identify its slope.
5x +3y= 15
3y= -5x +15
Divide both sides by 3:
[tex]y = - \frac{ 5}{3} x + 5[/tex]
Thus, the slope of the given line is [tex] - \frac{5}{3} [/tex]
The slope of a perpendicular line is the negative reciprocal of the given line. In simpler terms, the slope of the perpendicular line can be found by flipping the denominator and numerator, and by multiplying -1 afterwards.
Slope of perpendicular line= [tex] \frac{3}{5} [/tex]
Substitute the value of the slope into the equation:
[tex]y = \frac{3}{5} x + c[/tex]
To find the value of c, substitute a pair of coordinates the line passes through.
When x= -1, y= 2,
[tex]2 = \frac{3}{5} ( - 1) + c[/tex]
Solve for c:
[tex]c = 2 + \frac{3}{5} [/tex]
[tex]c = \frac{13}{5} [/tex]
Thus, the equation of the line described is [tex]y = \frac{3}{5} x + \frac{13}{5} [/tex].
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