What does the graph of a function in the form y = mx + b look like?
line
point
parabola
circle
line : )
Thank you soooooo much!
The graph of a function in the form y = mx + b represents a linear function. This means that the graph will be a straight line.
To understand this, let's break down the equation:
- "m" represents the slope of the line, which determines the steepness of the line. It tells us how much y increases (or decreases) for each unit increase in x. If m is positive, the line slopes upwards as x increases, and if m is negative, the line slopes downwards.
- "b" represents the y-intercept, which is the y-coordinate where the line intersects the y-axis (when x = 0).
Knowing the slope and y-intercept, you can easily sketch the graph. Start by plotting the y-intercept point (0,b) on the y-axis. Then, using the slope, you can move to other points on the graph. For example, if the slope is 2, you can interpret it as moving up 2 units and right 1 unit (or down 2 units and left 1 unit if the slope is -2). Connect these points, and you will have a straight line.
Therefore, the graph of a function of the form y = mx + b is always a line.