Yazmin T. answered • 11/02/20

Math Tutor / Spanish Tutor / Track and Field Throws Coach

Equation: -3x + 2y = 12 Point: (1, -5)

Point Slope form formula: y - y_{1} = m(x - x_{1})

For this problem, we need to find slope, x_{1} and y_{1} and x_{2} and y_{2}.

To find the slope, we use the use the equation that is given to us. We have to change this equation into slope-intercept form, meaning it needs to look like this y = mx + b

To do this, you need to get y all by itself. So:

-3x + 2y = 12

+3x + 3x

______________

2y = 3x + 12 Divide all terms by 2 to get y by itself

y = 2/3x + 12

So our new equation is y= 2/3x + 12.

****Reminder: m is the slope and it is ALWAYS next to the x ONLY IF it is in the form above.

So, slope = 2/3. BUT our question is asking for a line that is PERPENDICULAR. So we need the slope that is PERPENDICULAR. To fin this slope, we take the slope we found and find the opposite reciprocal, meaning we do a flip and sign change. So it we flip 2/3, we get 3/2 and if we do a sign sign change, we go from positive to negative. Final slope will be -3/2.

Now we need to find x_{1} and y_{1} and x_{2} and y_{2}. A point is given to us already. We are going to label this point (x_{1} , y_{2}). So, x_{1} = 1 and and y_{1} = -5

Now that we have all this information, we plug and chug into our point slope formula and solve.

y - y_{1} = m(x - x_{1})

y - (-5) = -3/2(x - 1)

y + 5 = -3/2x + 3/2

- 5 - 5 Need to find a common denominator. 5 = 10/2

So -10/2 + 3/2 = -7/2

y = -3/2x - 7/2

So our final answer is y = -3/2x - 7/2