Question

graph this line using the slope and y-intercept;
y = -7x + 8
click to select points on the graph.

Explanation:

Step1: Identify y - intercept

The equation of the line is in the slope - intercept form \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. For the equation \(y=-7x + 8\), the \(y\) - intercept \(b = 8\). This means the line intersects the \(y\) - axis at the point \((0,8)\). So we plot the point \((0,8)\) on the graph.

Step2: Use the slope to find another point

The slope \(m=-7\), which can be written as \(\frac{-7}{1}\) (or \(\frac{7}{-1}\)). The slope is the ratio of the change in \(y\) (\(\Delta y\)) to the change in \(x\) (\(\Delta x\)), i.e., \(m=\frac{\Delta y}{\Delta x}\). Starting from the \(y\) - intercept \((0,8)\), if we take \(\Delta x = 1\) (move 1 unit to the right along the \(x\) - axis), then \(\Delta y=-7\) (move 7 units down along the \(y\) - axis). So the new point is \((0 + 1,8-7)=(1,1)\). We can also use the negative of the slope: if \(\Delta x=- 1\) (move 1 unit to the left), then \(\Delta y = 7\) (move 7 units up), giving the point \((0-1,8 + 7)=(-1,15)\) (but \((1,1)\) is more convenient for graphing on the given grid).

Step3: Draw the line

After plotting the points \((0,8)\) and \((1,1)\) (or other points found using the slope), we draw a straight line passing through these points.

To graph the line \(y = - 7x+8\):

1. Plot the \(y\) - intercept: Mark the point \((0,8)\) on the coordinate plane (where the \(x\) - coordinate is 0 and the \(y\) - coordinate is 8).
2. Use the slope: From the point \((0,8)\), since the slope is \(-7=\frac{-7}{1}\), move 1 unit to the right (increase \(x\) by 1) and 7 units down (decrease \(y\) by 7) to get the point \((1,1)\). (You can also move 1 unit to the left and 7 units up to get \((-1,15)\), but \((1,1)\) is within the visible grid better).
3. Draw a straight line connecting the points \((0,8)\) and \((1,1)\) (and extending it in both directions).

Answer:

The line is graphed by first plotting \((0,8)\) (the \(y\) - intercept) and then using the slope \(-7\) to find another point (e.g., \((1,1)\)) and drawing a straight line through these points.