Question: Graph the line with slope \(-3\) passing through the point \((1, -4)\). [Graphing tools:…

Graph the line with slope \(-3\) passing through the point \((1, -4)\).

[Graphing tools: Eraser, Pencil, Line]

Explanation Check

Solution

To find the equation of the line with slope \(-3\) passing through the point \((1, -4)\), we use the point-slope form equation: \[ y - y_1 = m(x - x_1) \] Substitute the given slope \(m = -3\) and point \((x_1, y_1) = (1, -4)\) into the equation: \[ y - (-4) = -3(x - 1) \] Simplify the equation: \[ y + 4 = -3x + 3 \] Subtract 4 from both sides: \[ y = -3x + 3 - 4 \] Combine the constant terms: \[ y = -3x - 1 \] So, the equation of the line is \(y = -3x - 1\). You can graph this line by plotting the point \((1, -4)\) and using the slope to determine another point. From \((1, -4)\), move down 3 units and 1 unit to the right to find another point, and draw the line through these points.