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write an equation for the line passing through the point (3,5) and perpendicular to the line y=-1/3x+5

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y= 3x -4

Step-by-step explanation:

The equation of a line can be written in the form of y=mx +c, where m is the slope and c is the y-intercept. This is also known as the slope-intercept form.

$$y = - \frac{1}{3} x + 5$$

Since the given equation is in the slope-intercept form, we can identify its slope from the coefficient of x.

Slope= -⅓

The product of the slopes of perpendicular lines is -1.

Slope of perpendicular line

$$= - 1 \div ( - \frac{1}{3} )$$

$$= - 1 \times ( - \frac{3}{1} )$$

= 3

Thus, the equation of the perpendicular line is given by:

y= 3x +c

Substitute a pair of coordinates that the line passes through to find the value of c.

When x= 3, y= 5,

5= 3(3) +c

5= 9 +c

Minus 9 on both sides:

c= 5 -9

c= -4

Hence, the equation of the perpendicular line is y= 3x -4.