Question

write an equation of the line passing through (-3,2) and (6,3). give the answer in standard form. the equation of the line in standard form is \boxed{}

Explanation:

Step1: Find the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1,y_1)=(-3,2)\) and \((x_2,y_2)=(6,3)\). So, \( m=\frac{3 - 2}{6 - (-3)}=\frac{1}{9} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-3,2)\) and \( m = \frac{1}{9} \), we get \( y - 2=\frac{1}{9}(x + 3) \).

Step3: Convert to standard form

First, multiply both sides by 9 to get rid of the fraction: \( 9(y - 2)=x + 3 \). Expand the left side: \( 9y-18=x + 3 \). Then, rearrange the terms to get \( x-9y=-21 \) (standard form is \( Ax + By = C \), where \( A\), \( B\), and \( C\) are integers and \( A\geq0 \)).

Answer:

\(x - 9y=-21\)