Question

graph each equation. 5. $y = -5x + 1$

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = -5x + 1 \) is in slope - intercept form \( y=mx + b \), where \( m=-5 \) (slope) and \( b = 1 \) (y - intercept). The y - intercept is the point where the line crosses the y - axis, so when \( x = 0 \), \( y=1 \). So we have a point \( (0,1) \).

Step2: Use the slope to find another point

The slope \( m=\frac{\text{rise}}{\text{run}}=- 5=\frac{-5}{1} \). From the point \( (0,1) \), we can go down 5 units (because the rise is - 5) and then 1 unit to the right (because the run is 1). So starting from \( (0,1) \), moving down 5 gives \( y=1 - 5=-4 \) and moving right 1 gives \( x = 0+1 = 1 \). So we get the point \( (1,-4) \). We can also go up 5 units and left 1 unit (since \( \frac{5}{-1}=-5 \)). From \( (0,1) \), moving up 5 gives \( y = 1+5 = 6 \) and moving left 1 gives \( x=0 - 1=-1 \), so we get the point \( (-1,6) \).

Step3: Plot the points and draw the line

Plot the points \( (0,1) \), \( (1,-4) \), and \( (-1,6) \) on the coordinate plane. Then draw a straight line passing through these points.

(Note: Since the problem is to graph the equation, the final answer is the graph of the line \( y=-5x + 1 \) passing through the points we found. But if we were to describe the key points for graphing: the y - intercept is at \( (0,1) \) and another point is \( (1,-4) \) or \( (-1,6) \) and the line connects these points with a slope of - 5.)

Answer:

The graph of \( y=-5x + 1 \) is a straight line with a y - intercept at \( (0,1) \) and a slope of - 5, passing through points like \( (0,1) \), \( (1,-4) \), and \( (-1,6) \) (the line is drawn through these plotted points).