# Write the equation of the line in slope-intercept form that passes through the point (4,-6) and is perpendicular to the line -2x +5y= 8

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The product of the slope of two perpendicular lines is equal to -1.

Determine the slope of the line represented by -2x + 5y = 8.

-2x + 5y = 8

=> 5y = 2x + 8

=> y = (2/5)*x + 8/5

This is in the slope-intercept form and the slope of the line is 2/5

The slope of a line perpendicular to this line is -5/2.

If the line passes through the point (4, -6) its equation is (y + 6)/(x - 4) = -5/2

=> 2y + 12 = 20 - 5x

=> 5x + 2y - 8 = 0

**The required equation is 5x + 2y - 8 = 0**

To reflect the above answer in slope-intercept form, having determined that the slope (m) = `-5/2` - ( the negative recipricol of the slope of the first equation which was `2/5` ) we can determine that `5x+2y-8=0` becomes `y=-5/2 x+4` ` `

Refer to the links below for guidance.

**Ans: y=`-5/2` x +4**