Question

What is the equation in point-slope form of a line that passes through the points (5, −3) and (−2, 9)?

a. y−3=−2(x 5)
b. y 3=−127(x−5)
c. y 3=−2(x−5)
d. y−3=−127(x 5)

Answer 1

To find the point-slope form equation of the line through (5, −3) and (−2, 9), calculate the slope and use one of the points. The slope is −12/7, leading to y−3=−12/7(x−5) as the correct point-slope form equation.

Step-by-step explanation:

The question asks for the equation of a line in point-slope form that passes through the points (5, −3) and (−2, 9). To find this equation, we need to calculate the slope (m) of the line using the given points and then use one of the points to write the equation.

To calculate the slope, we use the formula m=(y2−y1)/(x2−x1). Substituting the given points into this formula, we have m=(9−(−3))/(−2−5)=(9+3)/(−2−10)=(12)/(−7)=−12/7.

Now that we have the slope, the point-slope form equation is given by y−y1=m(x−x1), where (x1, y1) is one of the points and m is the slope. Using the point (5, −3), our equation becomes y−(−3)=−12/7(x−5). Simplifying, the equation is y+3=−12/7(x−5). Hence, the correct answer is (d): y−3=−12/7(x−5).