Write an equation of the line in slope-intercept form that is perpendicular to 4x + 8y = 16 and passes through (-5, 7)

To find the equation of the line in slope-intercept form that is perpendicular to 4x + 8y = 16 and passes through (-5, 7), we need to find the slope of the line perpendicular to 4x + 8y = 16. We can do that by finding the line in slope-intercept form, then finding the slope of the perpendicular line (which is the opposite reciprocal).

4x + 8y = 16

8y = -4x + 16

y = -0.5x + 2

The opposite reciprocal of -1/2 is 2. That means that we know the slope of our line.

That means that the slope of our line is 2, and the equation so far is y = 2x + b. Now we need to find the y intercept. Now, since we know one point that the line goes through, we can substitute the value of x and y into the equation. The equation becomes:

7 = -10 + b

That means that b = 17, meaning that the equation of the line is y = 2x + 17.

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