question graph the line passing through (6,1) whose slope is m = 3. provide your answer below:

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Given $(x_1,y_1)=(6,1)$ and $m = 3$, we have $y - 1=3(x - 6)$.

Step2: Expand the equation

Expand $y - 1=3(x - 6)$ to get $y-1 = 3x-18$. Then, solve for $y$: $y=3x - 17$.

Step3: Find the y - intercept

Set $x = 0$ in $y=3x - 17$. Then $y=-17$. So the y - intercept is $(0,-17)$.

Step4: Use the slope to find another point

Starting from the point $(6,1)$, since the slope $m = 3=\frac{\Delta y}{\Delta x}$, if we move 1 unit to the right ($\Delta x = 1$), we move 3 units up ($\Delta y=3$). So another point is $(6 + 1,1+3)=(7,4)$.

Step5: Graph the line

Plot the points $(6,1)$, $(0,-17)$ and $(7,4)$ on the coordinate plane and draw a straight - line passing through them.

Answer:

The graph of the line $y = 3x-17$ passing through the point $(6,1)$ with slope $m = 3$ is drawn by plotting the points $(6,1)$, $(0,-17)$ and $(7,4)$ and connecting them with a straight line.