To write an equation for a line, we need to understand Slope Intercept Form (SIF), how to find the slope, and how to find the y-intercept.
SIF is y=mx+b, where m is the slope of a line and b is the y-intercept. We should simply substitute the values in to that equation to find the equation of our line.
The slope of a line is often referred to as "rise over run." This comes from how you find slope. To find slope, you should put the change in the y-value over the change in the x-value from 2 points. Then, you should simplify the fraction. If the line travels in a negative direction, like it is here, we should make the fraction negative.
Between the 2 red dots, it goes down 4 and right 6. This means our slope is -4/6, which can be simplified to -2/3. Now, we can fill in the "m" for our equation.
y=-2/3x+b
Finally, we need to solve for our y-intercept. The y-intercept is the value of y when x=0. It can be seen on a graph as the point where the line crosses the y-axis. In this case, we can see that it is -3. Now, we can substitute that in for "b."
y=-2/3x-3
Using the logic above, we can see that the equation for this line is y=-2/3x-3.
