Question

a line passes through the point \\((-2, -5)\\) and has a slope of \\(-6\\). write an equation for this line.

Explanation:

Identify the given parameters

We are given a point through which the line passes and the slope of the line:

• Given point: \((x_1, y_1) = (-2, -5)\)
• Given slope: \(m = -6\)

Apply the point-slope formula

Using the Linear Equations knowledge point, we set up the point-slope equation of a line:

$$ y - y_1 = m(x - x_1) $$

Substituting the given values:

$$ y - (-5) = -6(x - (-2)) $$

Simplifying the signs:

$$ y + 5 = -6(x + 2) $$

Convert to slope-intercept form

Using the Slope-Intercept Form knowledge point

$$
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$$

Answer:

\(y = -6x - 17\)