Question

graph the line with slope -1 passing through the point (-4, -5).

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 \(m=-1\), \(x_1 = - 4\), \(y_1=-5\), we have \(y+5=-(x + 4)\).

Step2: Simplify the equation

Expand the right - hand side: \(y+5=-x - 4\). Then solve for \(y\): \(y=-x-9\).

Step3: Find another point

Let \(x = 0\), then \(y=-0 - 9=-9\). So another point on the line is \((0,-9)\).

Step4: Plot the points and draw the line

Plot the points \((-4,-5)\) and \((0,-9)\) on the coordinate plane. Then draw a straight line passing through these two points.

Answer:

Plot the point \((-4,-5)\). Using the slope \(m = - 1\) (which means for every 1 unit increase in \(x\), \(y\) decreases by 1 unit), find another point (e.g., \((0,-9)\)) and draw a line through them.