Find the Equation Using Two Points (-3,6) , (3,-1)

Problem

(−3,6),(3,−1)

Solution

1. Identify the coordinates of the two points as ((x_1),(y_1))=(−3,6) and ((x_2),(y_2))=(3,−1)

2. Calculate the slope m using the formula m=((y_2)−(y_1))/((x_2)−(x_1))

m=(−1−6)/(3−(−3))

m=(−7)/6

3. Use the point-slope form y−(y_1)=m*(x−(x_1)) with the point (−3,6)

y−6=−7/6*(x−(−3))

4. Distribute the slope on the right side of the equation.

y−6=−7/6*(x+3)

y−6=−7/6*x−21/6

5. Simplify the fraction 21/6 by dividing both numerator and denominator by 3.

y−6=−7/6*x−7/2

6. Isolate y by adding 6 to both sides to convert the equation to slope-intercept form y=m*x+b

y=−7/6*x−7/2+6

7. Find a common denominator to combine the constant terms, using 6=12/2

y=−7/6*x−7/2+12/2

y=−7/6*x+5/2

Final Answer

y=−7/6*x+5/2

Want more problems? Check here!