Question

write an equation of the line that passes through a pair of points: (-5, -2), (4, 5)
a. $y = \frac{7}{9}x - \frac{17}{9}$
c. $y = \frac{7}{9}x + \frac{17}{9}$
b. $y = \frac{7}{9}x - \frac{9}{17}$
d. $y = -\frac{7}{9}x + \frac{17}{9}$
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \( (x_1, y_1) = (-5, -2) \) and \( (x_2, y_2) = (4, 5) \) is given by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Substituting the values, we get \( m=\frac{5 - (-2)}{4 - (-5)}=\frac{5 + 2}{4 + 5}=\frac{7}{9} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \( (4,5) \) (we could also use \( (-5,-2) \)).
Substituting \( m = \frac{7}{9} \), \( x_1 = 4 \) and \( y_1 = 5 \) into the point - slope form:
\( y - 5=\frac{7}{9}(x - 4) \)

Step3: Simplify the equation

First, distribute the \( \frac{7}{9} \) on the right - hand side:
\( y - 5=\frac{7}{9}x-\frac{28}{9} \)
Then, add 5 to both sides. We know that \( 5=\frac{45}{9} \), so:
\( y=\frac{7}{9}x-\frac{28}{9}+\frac{45}{9} \)
\( y=\frac{7}{9}x+\frac{- 28 + 45}{9} \)
\( y=\frac{7}{9}x+\frac{17}{9} \)

Answer:

C. \( y = \frac{7}{9}x + \frac{17}{9} \)