Question

graph this line using the slope and y-intercept:
y = 8x + 1
click to select points on the graph.

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=8x + 1\), \(b = 1\). So the line crosses the y - axis at the point \((0,1)\).

Step2: Use the slope to find another point

The slope \(m\) in \(y=mx + b\) is 8, which can be written as \(\frac{8}{1}\). The slope is \(\frac{\text{rise}}{\text{run}}\), so from the y - intercept \((0,1)\), we rise 8 units (move up 8) and run 1 unit (move right 1). So the next point is \((0 + 1,1+8)=(1,9)\). We can also go in the opposite direction: from \((0,1)\), run - 1 (move left 1) and rise - 8 (move down 8) to get the point \((- 1,1 - 8)=(-1,-7)\) (though this point may be outside the given graph's visible range).

Step3: Plot the points and draw the line

Plot the points \((0,1)\) and \((1,9)\) (and other points if needed) on the coordinate plane and draw a straight line through them.

To graph the line \(y = 8x+1\):

1. Plot the y - intercept: Mark the point \((0,1)\) on the y - axis.
2. Use the slope: From \((0,1)\), move 1 unit to the right (run = 1) and 8 units up (rise = 8) to get the point \((1,9)\). Plot this point.
3. Draw a straight line connecting \((0,1)\) and \((1,9)\) (and extend it as needed).

Answer:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=8x + 1\), \(b = 1\). So the line crosses the y - axis at the point \((0,1)\).

Step2: Use the slope to find another point

The slope \(m\) in \(y=mx + b\) is 8, which can be written as \(\frac{8}{1}\). The slope is \(\frac{\text{rise}}{\text{run}}\), so from the y - intercept \((0,1)\), we rise 8 units (move up 8) and run 1 unit (move right 1). So the next point is \((0 + 1,1+8)=(1,9)\). We can also go in the opposite direction: from \((0,1)\), run - 1 (move left 1) and rise - 8 (move down 8) to get the point \((- 1,1 - 8)=(-1,-7)\) (though this point may be outside the given graph's visible range).

Step3: Plot the points and draw the line

Plot the points \((0,1)\) and \((1,9)\) (and other points if needed) on the coordinate plane and draw a straight line through them.

To graph the line \(y = 8x+1\):

1. Plot the y - intercept: Mark the point \((0,1)\) on the y - axis.
2. Use the slope: From \((0,1)\), move 1 unit to the right (run = 1) and 8 units up (rise = 8) to get the point \((1,9)\). Plot this point.
3. Draw a straight line connecting \((0,1)\) and \((1,9)\) (and extend it as needed).