Write an equation for the line that is perpendicular to Y=-3/7x+4 and passes through (-4,-5)

9514 1404 393

  y = 7/3x +13/3

Step-by-step explanation:

The equation of the given line is in slope-intercept form (y=mx+b), so we can see the slope (m) is -3/7. The slope of the perpendicular line is the opposite reciprocal of this, so is ...

  m = -1/(-3/7) = 7/3

The y-intercept of the perpendicular line can be found from ...

  b = y -mx

  b = -5 -(7/3)(-4) = -15/3 +28/3 = 13/3

Then the slope-intercept equation of the perpendicular line is ...

  y = mx +b

  y = 7/3x +13/3

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Additional comment

You can get there a little faster using the point-slope form of the equation of a line. For slope m and point (h, k) that form is ...

  y -k = m(x -h)

For our perpendicular line, the equation is ...

  y +5 = 7/3(x +4)