Using the graph, derived the equation of the line in slope intercept form coordinates are (0,-4) (1,-1)

1 answer

To derive the equation of the line in slope-intercept form y=mx+b using the given coordinates (0,4) and (1,1), let's follow these steps:

  1. Identify the coordinates:

    • Point 1: (0,4)
    • Point 2: (1,1)
  2. Calculate the slope (m): The formula for the slope m between two points (x1,y1) and (x2,y2) is: m=y2y1x2x1 Substituting the coordinates: m=1(4)10=1+41=31=3

  3. Use the slope and one of the points to find the y-intercept (b): We can use the y-intercept from point (0, -4) directly: Since the line passes through (0, -4), the y-intercept b is 4.

  4. Write the equation in slope-intercept form: Now that we have m=3 and b=4, we can substitute these values into the slope-intercept formula: y=3x4

Thus, the equation of the line in slope-intercept form is: y=3x4