What is the equation of the line in simplest standard form that passes through (3, -3) and (1, 2)?

What is the equation of the line in simplest standard form that passes through (3, -3) and (1, 2)?

• A. x + y = 0
• B. 5x + 2y = 9
• C. 3x - y = 12
• D. y = -2x + 3

Answer: (B)

To find the equation of the line that passes through the points (3, -3) and (1, 2), we first need to determine the slope of the line using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Substituting the given points (1, 2) as \( (x_1, y_1) \) and (3, -3) as \( (x_2, y_2) \): - \( m = \frac{-3 - 2}{3 - 1} = \frac{-5}{2} \) Now that we have the slope, we can use the point-slope form of the equation of a line, which is \( y - y_1 = m(x - x_1) \). Using the point (3, -3) for \( (x_1, y_1) \): \[ y - (-3) = -\frac{5}{2}(x - 3) \] This simplifies to: \[ y + 3 = -\frac{5}{2}x + \frac{15}{2} \] Subtract

To find the equation of the line that passes through the points (3, -3) and (1, 2), we first need to determine the slope of the line using the formula ( m = \frac{y_2 - y_1}{x_2 - x_1} ).

Substituting the given points (1, 2) as ( (x_1, y_1) ) and (3, -3) as ( (x_2, y_2) ):

• ( m = \frac{-3 - 2}{3 - 1} = \frac{-5}{2} )

Now that we have the slope, we can use the point-slope form of the equation of a line, which is ( y - y_1 = m(x - x_1) ). Using the point (3, -3) for ( (x_1, y_1) ):

[

y - (-3) = -\frac{5}{2}(x - 3)

]

This simplifies to:

[

y + 3 = -\frac{5}{2}x + \frac{15}{2}

]

Subtract