Question

graph the line.
y = -5x + 3

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-5x + 3\), \(b = 3\). So the line crosses the y - axis at \((0,3)\). Plot the point \((0,3)\) on the graph.

Step2: Determine slope

The slope \(m=-5=\frac{-5}{1}\). The slope is the rise over run. From the y - intercept \((0,3)\), move down 5 units (because the rise is - 5) and then 1 unit to the right (run is 1). This gives the point \((1,3 - 5)=(1,-2)\). Plot this point.

Step3: Draw the line

Use a straightedge to draw a line through the two points \((0,3)\) and \((1,-2)\). Extend the line in both directions to show the entire line.

Answer:

The line \(y = - 5x+3\) is graphed by plotting the y - intercept \((0,3)\), using the slope \(-5\) to find another point \((1, - 2)\), and then drawing a straight line through these points (and extending it).