Graphing Linear Function.

Graphing Linear Function Since times of Euclid students know that to draw the straight line we don’t need to plot numerous dots. We need just two points to produce unique line: y = ax + b or y = slope ·x + y-intercept b is y-intercept that indicates point where line crosses y-axis. a is a number that indicates rate of change or slope, Note that slope in equation is multiplies by x, while y-intercept is added and stays by itself

We can pick any two values of x and find corresponding values of y, but the easiest is to use point of y-intercept (0, 3). Slope is rate of change of y depending on x. Let’s graph linear function with y-intercept 3 and slope - 4 y = 3 + ¯4x Now we’ll use slope to find the other point. Which means for 4 steps down we have to go 1 step right. Now we connect points and have our line! -4 1 Here is our second point

Examples of graphing linear function 1. Slope is give as fraction: Re-write equation in slope-intercept form: y = slope • x + y-intercept: Identify y-intercept = -6 So our first point will be on the y-axis (0, -6) Identify slope = Slope is positive, so from our y-intercept we have to go up. 3 in numerator and 5 and denominator tell us that for every 3 steps up we have to make 5 steps to the right: +3 5

Examples of graphing linear function 2. Slope is give as fraction: Identify y-intercept = 6 So our first point will be on the y-axis (0, 6) Identify slope = Slope is negative, so from our y-intercept we have to go down. -2 7 2 in numerator and 7 in denominator tell us that for every 2 steps down we have to make 7 steps to the right:

Examples of graphing linear function 3. Slope is equal to 0: Identify y-intercept = 2 So our first point will be on the y-axis (0, 2) Slope is 0 – we don’t go either up or down from our starting point - y = 2 If slope = 0 it is HORIZONTAL line y = b Re-write equation in slope-intercept form:

Examples of graphing linear function 4. Y-intercept is equal to 0: Re-write equation in slope-intercept form: Identify y-intercept =0 So our first point will be origin (0,0). Identify slope = Slope is positive, so from our y-intercept we have to go up. 1 in numerator and 2 and denominator tell us that for every1 steps up we have to make 2 steps to the right: +1 2

Examples of graphing linear function 5. Identity line: Re-write equation in slope-intercept form: y = slope • x + y-intercept: Identify y-intercept = 0 So our first point origin (0,0) Identify slope = 1 Slope is positive, so from our y-intercept we have to go up. 1 in numerator and 1 and denominator tell us that for every 1 steps up we have to make 1 steps to the right: 1 1 Re-write slope as fraction by putting 1 into denominator:

Examples of graphing linear function 6. Sometimes slope and y-intercept don’t look that pretty: In this situation it can be easier to use points other than y-intercept: (10.2.8) (20, 10.1) Pick any two values of x and compute corresponding values of y: So we have now two points (10, 2.8) and (20, 10.1) to draw the line

How do the graph of linear functions compare? Lines with equal slopes are parallel Lines with the same. y-intercept intersect in the same point on y-axis