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okay well for a) the line is perpendicular meaning that it need to go the opposite way of 2/3x+6 so in the new equation would have a negative value times x. also when you are trying to find a perpendicular line i believe you use the inverse of the slope meaning that you would have -3/2 time x. Then you  know that the line goes through (-6,4) so you just replace x with -6, add a varible (for example n) and then set the equation equal to 4 since 4 should be the y value that you get when you plug in 4. so it should look like

(-3/2)-6+n=4   you're doing this so that you can figure out the x intercept. Move the n to the right and subtract 4 from both sides, and then solve the numbers on the left. (-3/2)-6 =9 and then 9-4=5 so the y intercept you get is five. then the new eqaution you shoud have is (-3/2)x-5=y

b.) well the x values are both positive meaning that you subtract so there is a distance of 2 units between then and the y values have a negative number and a positive number meaning you add so there is a distance of 5. The slope should be rise over run so the slope is 5/2 and then you can plug in a value of x to find the y intercept. lets use (6,-3) so

(5/2)6+n=-3. isolate the variable and tadaa you get a y intercept of -18. so the equation for the second one is (5/2)x-18=y

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225