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- 7)?
What is an equation of the line that is perpendicular to 3x+y=-5 and passes through the point (3,
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URGENT PLEASE

Answer 1

`y=(1)/(3)x-8`

Explanation:

• We know that when two lines are perpendicular, their slopes are negative reciprocals. The following formula shows this fact:

`m_(2)=-(1)/(m_(1) )`, where

• m2 is the slope of the line we're trying to find
• m1 is the slope of the line we're given

Step 1: Currently 3x + y = -5 is in standard form, but we can isolate y to convert the line to slope-intercept form (y = mx + b) to find the slope, m:

3x + y = -5

y = -3x + 5

Thus, the slope of the first line is -3. We plug in -3 for m1 in the perpendicular slope formula to find m2 or the slope of the line we're still trying to find:

m2 = -1 / -3

m2 = 1/3

Step 2: Now that we know the slope of the other line, we plug in the point (3, -7) for x and y and 1/3 for m in the slope-intercept form. Then, we must solve for b to find the y-intercept of the other line:

-7 = 1/3(3) + b

-7 = 1 + b

-8 = b

Thus, the equation of the line that is perpendicular to 3x + y = -5 and passes through (3, -7) = y = 1/3x - 8