Write the equation of a line perpendicular to 3x+2y=8 that contains (0,3

Step-by-step explanation:

In the first step, re-write the equation of the given line in slope-y_intercept form in order to see clearly what its slope is. This means to solve for "y" in the equation:

So the slope of the given line is ""

Recall that the perpendicular line to a given one has a slope that equals the "opposite of the reciprocal"  of the original line's slope. This means that the slope of the perpendicular line to our original line must be: ""

We now try to write the equation of the perpendicular line using its slope-y_intercept form, and notice that all we need to find is what is is y_intercept (b):

To determine "b" we use the information they give us about this perpendicular line containing the point (0,3):

Then we found that b must be 3, and we can now write the complete equation of the perpendicular line:

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