equation of line of best fit - Tess plants flowers every year, and she noticed that her flowers tend to bloom earlier when the spring weather is warmer. She collected data for the past 6 years on the average March temperature where she lives, and the date in April her first flowers bloomed this year. A line was fit to the data to model the relationship.

Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

Let us say that below is the graph.

You know that an equation for a linear model is in the form y = mx + b where a is the slope of the line and b is the y-intercept.

Notice that the y-intercept or the point where the line intersects the y-axis is 28.

Now about the slope of the line. How can you say if you have a positive slope or a negative slope? Can you see how when the values of x (average march temperature) increases, the value of y ( date in April of first bloom) decrease? This means we have a negative slope.

Graphically, a negative slope means that as the line on the line graph moves from left to right, the line falls

We find the slope of the line using the formula m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

Take two points on the blue line, Say (0,28) and (2,24)

Plug in x_{1}=0, y_{1} = 28, x_{2} = 2, y_{2} = 24

So, plugging in these values m = \frac{24-28}{2-0} = \frac{-4}{2} = -2

Plug in m = -2, b = 28 in the equation y = m x+ b to get the equation of the line.

If you want to find the date in April for which the average March temperature is 5.5^\circ C just plug in x = 5.5 in the equation you got, to get the date.