# Find the equation of the line (in slope intercept form) through (-5,8) and perpendicular to the line 4x + 2y = 8

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We re-write the equation in slope-intercept form to find the slope of the ``equation. `4x+2y=8` We subtract 4x from each side and get `2y=8-4x=-4x+8` We divide both sides by 2 and its `y=-2x+4`

The equation we seek is perpendicular to this so its slope should be the negative reciprocal of -2, which is `1/2`

Now that we know the slope(m), we can find the intercept (b) by inserting the ordered pair (-5,8) into the equation y=mx+b

`y=mx+b->8=1/2(-5)+b=-2 1/2+b` We add `2 1/2` to each side and we get `10 1/2=b`

The equation in slope intercept form is `y=1/2 x+10 1/2`

The equation of a line in slope intercept form is y = mx + c where m is the slope and c is the intercept.

Rewrite the equation of the line 4x + 2y = 8 to determine its slope.

2y = 8 - 4x

y = -2x + 4

The slope of this line is -2.

As we have to determine the equation of a line perpendicular to this line remember that the product of slope of two perpendicular lines is -1.

The slope of the required line is 1/2.

As it passes through the point (-5,8).

(y - 8)/(x + 5) = 1/2

y - 8 = x/2 + 5/2

y = x/2 + 21/2

The required equation is y = x/2 + 11.5