Question

graph the line:
y = -5x + 2

Explanation:

Step1: Identify the y - intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=-5x + 2\), when \(x = 0\), \(y=2\). So the y - intercept is the point \((0,2)\). We can plot this point on the graph (on the y - axis, at \(y = 2\)).

Step2: Use the slope to find another point

The slope \(m=-5=\frac{- 5}{1}\). The slope is the rise over run, which means for a change in \(x\) (run) of \(1\) unit, the change in \(y\) (rise) is \(-5\) units. Starting from the y - intercept \((0,2)\), if we move \(x = 1\) unit to the right (run = 1), we move \(y=-5\) units (down 5 units) to get the point \((0 + 1,2-5)=(1,-3)\). We can also use a negative run: if we move \(x=- 1\) unit (1 unit to the left), the rise is \(-5\times(-1) = 5\) units (up 5 units), so we get the point \((0-1,2 + 5)=(-1,7)\).

Step3: Draw the line

After plotting two points (e.g., \((0,2)\) and \((1,-3)\) or \((0,2)\) and \((-1,7)\)), we can draw a straight line passing through these points to graph the line \(y=-5x + 2\).

Answer:

To graph \(y = - 5x+2\), plot the y - intercept \((0,2)\) and use the slope \(-5\) to find another point (e.g., \((1,-3)\) or \((-1,7)\)) and draw a line through them. The key points are \((0,2)\) and other points determined by the slope.