Given the equation:
y = ⅔ x - 1
Using the slope intercept form:
y = mx + b
where m is the slope and b is the y intercept
Therefore, the slope here is ⅔ , while the y intercept is (0, -1).
Using the slope formula:
[tex]\text{slope = }\frac{change\text{ in y}}{\text{change in x}}\text{ = }\frac{rise\text{ }}{\text{run}}[/tex]
Since the slope is ⅔ , we can say that if x changes by 3, y will change by 2. This means the numerator indicates how many steps to move up or down, while the denominator indicates how many steps to move left or right.
To graph the linear equation, y = ⅔ x - 1, find the point of the y intercept which is -1 in this case, and move from that point on x with 3 points, then move y with 2 points.
Now the graph will look like this:
