Question

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

Explanation:

Step1: Recall 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 $m=-7$ and $b = 6$, the equation of the line is $y=-7x + 6$.

Step2: Plot the y - intercept

The $y$-intercept is 6, so we plot the point $(0,6)$ on the coordinate plane (where $x = 0$ and $y=6$).

Step3: Use the slope to find another point

The slope $m=-7=\frac{-7}{1}=\frac{\text{rise}}{\text{run}}$. From the point $(0,6)$, we move down 7 units (because the rise is - 7) and then 1 unit to the right (because the run is 1). So we move from $(0,6)$ to $(0 + 1,6-7)=(1,-1)$. We can also move up 7 units and left 1 unit (since $\frac{7}{-1}$ is also equal to - 7) from $(0,6)$ to $(-1,13)$, but $(1,-1)$ is a more convenient point for graphing on the given grid.

Step4: Draw the line

Draw a straight line passing through the points $(0,6)$ and $(1,-1)$ (or other points found using the slope) to represent the line $y=-7x + 6$.

(Note: Since the problem is about graphing, the final answer is the graph of the line with equation $y = - 7x+6$ passing through $(0,6)$ and other points determined by the slope, but in terms of the equation and the key points for graphing, the equation is $y=-7x + 6$)

Answer:

The line has the equation $y=-7x + 6$, with a $y$-intercept at $(0,6)$ and another point (e.g., $(1,-1)$) used to draw the line. The graph is a straight line passing through these points with a slope of - 7.