The equation y = 2/3x + 9 is written in slope intercept, or y = mx + b. The m is the slope, and the b is the y intercept.
When a line is perpendicular to another, it meets it at a 90 degree angle. The slope of the line which is perpendicular to one with a given slope is the negative reciprocal of it, for example, if you had a line with slope 1/2, the slope of the line perpendicular to it would be -2.
So for this line, the negative reciprocal of 2/3 is -3/2. You now have one of the slots of the equation filled in, giving you:
y = -3/2x + b
Now, you just need to find b, as slope intercept leaves x and y as variables. Luckily, you are given a point that lays on the line; (-6, 5).
So to solve for b, you can substitute that point in, using -6 as x and 5 as y. That gives you:
5 = -3/2 (-6) + b
Now, just solve for b.
5 = -3/2 (-6) + b 5 = 9 + b b = -4
And there's your solution for b, which you can fill in, giving you your final answer of:
Answer: 5X + 8Y >= 300; intersection at (-20, 50) Step-by-step explanation: let t = work hours 0 < t < 30 X = time lawn mowing Y = time babysitting. X + Y < 30 5X + 8Y >= 300 We could solve... X < 30 - Y 5(30 - Y) + 8Y >=300 150 - 5Y + 8Y >= 300 3Y >=150 Y >=50 then X < -20 intersection at (-20, 50)
