Questions: Use two points on the given graph of a line to find the equation of the line in standard form.

Solution Steps

From the graph, we can identify two points on the line. Let's choose the points (-6, 6) and (0, -2).

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the points (-6, 6) and (0, -2): \[ m = \frac{-2 - 6}{0 - (-6)} = \frac{-8}{6} = -\frac{4}{3} \]

The point-slope form of the equation of a line is: \[ y - y_1 = m(x - x_1) \]

Using the point (0, -2) and the slope \( m = -\frac{4}{3} \): \[ y - (-2) = -\frac{4}{3}(x - 0) \] \[ y + 2 = -\frac{4}{3}x \]

The standard form of a line's equation is \( Ax + By = C \). We need to rearrange the equation: \[ y + 2 = -\frac{4}{3}x \] Multiply every term by 3 to clear the fraction: \[ 3y + 6 = -4x \] Rearrange to standard form: \[ 4x + 3y = -6 \]

Final Answer