Question

graph the line with slope 3 passing through the point $(2,-4)$.

Explanation:

Step1: Use the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \(m\) is the slope and \((x_1,y_1)\) is a point on the line. Given \(m = 3\), \(x_1=2\), and \(y_1=-4\), we have \(y+4 = 3(x - 2)\).

Step2: Simplify the equation

Expand the right - hand side: \(y+4=3x-6\). Then, solve for \(y\): \(y=3x-6 - 4\), so \(y = 3x-10\).

Step3: Find another point

Let \(x = 0\), then \(y=3\times0 - 10=-10\). So another point on the line is \((0,-10)\).

Step4: Plot the points and draw the line

Plot the points \((2,-4)\) and \((0,-10)\). Then, use a straight - edge to draw a line passing through these two points.

Answer:

Plot the point \((2,-4)\). Since the slope \(m = 3=\frac{\Delta y}{\Delta x}\), from the point \((2,-4)\), move 1 unit to the right (increase \(x\) by 1) and 3 units up (increase \(y\) by 3) to get another point \((3,-1)\). Also, from \((2,-4)\), move 1 unit to the left (decrease \(x\) by 1) and 3 units down (decrease \(y\) by 3) to get the point \((1,-7)\). Connect these points (or use the equation \(y = 3x-10\) to find more points) to graph the line.