Ethem S. answered • 10/13/19

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We need an equation in the form of

y = mx + b

First piece of information we have is "line that is perpendicular to 5x+2y = 12". So, what is the slope of this line? Let's write it in the slope/intercept form:

5x + 2y = 12 (Add -5x to both sides)

2y = 12 - 5x (divide both sides by 2)

y = 6 - 5/2 x = -5/2 x + 6

So, m (slope) is -5/2. The perpendicular line will have a slope of -1/m = -1 / (-5/2) = 2/5. Now we have

y = 2/5 x + b. So, what is b? We can use the second piece of information: "the line contains the point (2,3)" or for this line, when x = 2, y = 3. Let's substitute x = 2 and y = 3 in the equation and solve for b.

3 = (2/5)*2 + b

3 = 4/5 + b

b = 3 - 4/5 = 15/5 - 4/5 = 11/5

So, the line we are looking for is:

y = (2/5) x + 11/5