Graph the line with slope -3 passing through the point $(1,-1)$.
Answer
Finally, to graph the line, plot the point \((1,-1)\) and use the slope to find another point. Since the slope is -3, you can go down 3 units and to the right 1 unit from the point \((1,-1)\) to get to the point \((2,-4)\). Draw a line through these two points to graph the line.
Step 1 ：First, remember that the slope of a line in the form of \(y=mx+b\) is equal to \(m\). So, the line must take the form \(y=-3x+b\).
Step 2 ：Next, substitute the point \((1,-1)\) and solve for \(b\): \begin{align*} -1&=-3(1)+b\\ \Rightarrow\qquad -1&=-3+b\\ \Rightarrow\qquad 2&=b \end{align*}
Step 3 ：Therefore, the equation of the line is \(y=-3x+2\).
Step 4 ：Finally, to graph the line, plot the point \((1,-1)\) and use the slope to find another point. Since the slope is -3, you can go down 3 units and to the right 1 unit from the point \((1,-1)\) to get to the point \((2,-4)\). Draw a line through these two points to graph the line.
