Question: Graph the line passing through the given point and having the given slope. $(-3, -1)$, $m = 2$…

Graph the line passing through the given point and having the given slope.

$(-3, -1)$, $m = 2$

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Solution

To graph the line passing through the given point and having the given slope, we can use the point-slope form of a line, which is: \[ y - y_1 = m(x - x_1) \] Substitute the given point \((-3, -1)\) and the slope \(m = 2\) into the point-slope form. \[ y - (-1) = 2(x - (-3)) \] Simplify the equation: \[ y + 1 = 2(x + 3) \] Distribute the slope on the right side: \[ y + 1 = 2x + 6 \] Subtract 1 from both sides to solve for \(y\): \[ y = 2x + 6 - 1 \] \[ y = 2x + 5 \] The equation of the line is \(y = 2x + 5\).