Equation: -3x + 2y = 12 Point: (1, -5)
Point Slope form formula: y - y1 = m(x - x1)
For this problem, we need to find slope, x1 and y1 and x2 and y2.
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 x1 and y1 and x2 and y2. A point is given to us already. We are going to label this point (x1 , y2). So, x1 = 1 and and y1 = -5
Now that we have all this information, we plug and chug into our point slope formula and solve.
y - y1 = m(x - x1)
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