Question

graph the line using the slope and y-intercept.
graph the line through the point (0, 1), having a slope of -5.

Explanation:

Step1: Identify the y - intercept

The point \((0,1)\) is the y - intercept, so we start by plotting this point on the coordinate plane. The y - intercept is the point where the line crosses the y - axis, and its coordinates are \((0,b)\) where \(b\) is the y - intercept value. Here, \(b = 1\), so we mark the point \((0,1)\).

Step2: Use the slope to find another point

The slope \(m=- 5\) can be written as \(\frac{-5}{1}\) (since slope \(m=\frac{\text{rise}}{\text{run}}\)). The "rise" is the change in \(y\) and the "run" is the change in \(x\). Starting from the y - intercept \((0,1)\), for a slope of \(\frac{-5}{1}\), we move down 5 units (because the rise is - 5, which means a decrease in \(y\)) and then 1 unit to the right (because the run is 1, which means an increase in \(x\)).
Moving down 5 units from \(y = 1\) gives \(y=1-5=-4\), and moving 1 unit to the right from \(x = 0\) gives \(x = 0 + 1=1\). So the new point is \((1,-4)\).

Step3: Draw the line

Now that we have two points \((0,1)\) and \((1,-4)\), we can draw a straight line passing through these two points. We can also find more points by repeating the slope - based movement (for example, from \((1,-4)\), moving down 5 units and right 1 unit gives \((2,-9)\), etc.) to ensure the line is drawn accurately, but two points are sufficient to define a straight line.

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through \((0,1)\) and \((1,-4)\) (and other points obtained by the slope) as described above. If we were to write the equation of the line, it would be \(y=-5x + 1\) using the slope - intercept form \(y=mx + b\) where \(m=-5\) and \(b = 1\), but the main task here is graphing.)

Answer:

The line is graphed by first plotting the y - intercept \((0,1)\), then using the slope \(-5=\frac{-5}{1}\) to find another point (e.g., \((1,-4)\)) and drawing a straight line through these points. The equation of the line is \(y=-5x + 1\) (for reference), and the graph consists of a straight line passing through \((0,1)\), \((1,-4)\), \((2,-9)\), etc.