Question

graph the line with slope -7 and y-intercept 6.

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. Given that the slope $m=-7$ and the $y$-intercept $b = 6$, the equation of the line is $y=-7x + 6$.

Step2: Plot the $y$-intercept

The $y$-intercept is 6, so we start by plotting the point $(0,6)$ on the $y$-axis.

Step3: Use the slope to find another point

The slope $m=-7=\frac{-7}{1}$. The slope is $\frac{\text{rise}}{\text{run}}$, which means from the point $(0,6)$, we can go down 7 units (because the rise is - 7) and then right 1 unit (because the run is 1). So from $(0,6)$, moving down 7 units gives a $y$-coordinate of $6-7=-1$, and moving right 1 unit gives an $x$-coordinate of $0 + 1=1$. So we get the point $(1,-1)$.

Step4: Draw the line

Now that we have two points $(0,6)$ and $(1,-1)$, we can draw a straight line passing through these two points. We can also find more points for accuracy. For example, if we go left 1 unit from $(0,6)$ (run=-1) and up 7 units (rise = 7, since $\frac{-7}{1}=\frac{7}{-1}$), we get the point $(-1,13)$. Plotting additional points and drawing a line through them will give the graph of the line $y=-7x + 6$.

(Note: Since this is a graphing problem, the final answer is the graph of the line $y = - 7x+6$ with the $y$-intercept at $(0,6)$ and other points plotted using the slope to draw the line. However, in text - based form, we can describe the process as above.)

Answer:

The line is graphed by first plotting the point \((0, 6)\) (the \(y\)-intercept) and then using the slope \(-7=\frac{-7}{1}\) to find another point (e.g., \((1, - 1)\) by moving down 7 units and right 1 unit from \((0,6)\)) and drawing a straight line through these points. The equation of the line is \(y=-7x + 6\).