Question

1. write the equation of the line that passes through (-6, -2) and (-8, 1)

type a response

Explanation:

Step1: Find the slope (m)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let \((x_1, y_1)=(-6, -2)\) and \((x_2, y_2)=(-8, 1)\).
\( m=\frac{1 - (-2)}{-8 - (-6)}=\frac{1 + 2}{-8 + 6}=\frac{3}{-2}=-\frac{3}{2} \)

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((-6, -2)\) and \( m = -\frac{3}{2} \).
\( y - (-2)=-\frac{3}{2}(x - (-6)) \)
Simplify the left - hand side and the right - hand side:
\( y + 2=-\frac{3}{2}(x + 6) \)

Step3: Convert to slope - intercept form (\(y=mx + b\))

Expand the right - hand side: \( y+2 = -\frac{3}{2}x-9 \)
Subtract 2 from both sides: \( y=-\frac{3}{2}x-9 - 2 \)
\( y=-\frac{3}{2}x-11 \)

We can also write it in standard form (\(Ax + By = C\)):
Multiply through by 2 to get rid of the fraction: \( 2y=-3x - 22 \)
Then, \( 3x+2y=-22 \)

Answer:

The equation of the line in slope - intercept form is \( y = -\frac{3}{2}x-11 \) (or in standard form \( 3x + 2y=-22 \))