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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

you can't solve x because it is 2 linear equation and you only have one equation

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.