To find the equation of a line with slope $m = 2$ that passes through the point $(-4, -3)$, we use the point-slope form of a linear equation:

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

where $(x_1, y_1)$ is a given point on the line, and $m$ is the slope.

Substituting the given values:

$y - (-3) = 2(x - (-4))$

$y + 3 = 2(x + 4)$

$y + 3 = 2x + 8$

$y = 2x + 5$

Final Answer:

$y = 2x + 5$

This is the slope-intercept form of the equation of the line.

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Here are five related questions for further practice:

1. Find the equation of the line with slope $-3$ that passes through $(2, 5)$.
2. Find the equation of the line passing through points $(1,2)$ and $(3,6)$.
3. Convert the equation $3x - 2y = 6$ to slope-intercept form.
4. Determine the slope of the line perpendicular to $y = \frac{1}{2}x - 4$.
5. Find the x-intercept and y-intercept of the line $y = -\frac{2}{3}x + 4$.

Tip:

A line parallel to $y = mx + b$ has the same slope $m$, while a perpendicular line has a slope of $-\frac{1}{m}$.