Question 6(Multiple Choice Worth 40 points) (04.04 MC) Which of the following is the equation for the graph shown? graph of an e
llipse on a coordinate plane going through approximately 0 comma 6, 0 comma negative 6, 4 and one half comma 0 and negative 4 and one half comma 0 with points inside ellipse at 0 comma negative 4 and 0 comma 4, and lines y equals 9 and y equals negative 9 x squared over 20 plus y squared over 36 equals 1 x squared over 36 plus y squared over 20 equals 1 x squared over 20 minus y squared over 36 equals 1 x squared over 36 minus y squared over 20 equals 1
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- Slope-Intercept Form: y = mx+b, with m = slope and b = y-intercept
So perpendicular lines have <u>slopes that are negative reciprocals</u> to each other, but firstly we need to find the slope of the original equation. The easiest method to find it is to convert this standard form into slope-intercept.
Firstly, subtract 3x on both sides of the equation:
Next, divide both sides by -4 and your slope-intercept form of the original equation is
Now looking at this equation, we see that the slope is 3/4. Now since our new line is perpendicular, this means that <em>its slope is -4/3.</em>
Now that we have the slope, plug that into the m variable and plug in (-4,-5) into the x and y coordinates to solve for the b variable as such:
<u>In short, your new equation is y = -4/3x - 10 1/3.</u>