Question

approximate the best fitting line for the data. 7. 8.

Explanation:

Step1: Identify two points on the line

For the first graph, we can choose two points approximately on the line. Let's take $(0, 3.5)$ and $(4,0)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points: $m=\frac{0 - 3.5}{4-0}=-\frac{3.5}{4}= - 0.875$.

Step3: Find the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point $(0,3.5)$, $b = 3.5$.
The equation of the line is $y=mx + b$, so for the first graph $y=-0.875x + 3.5$.

For the second graph, choose two points, say $(0,1.5)$ and $(4,3)$.

Step4: Calculate the slope $m$

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m=\frac{3 - 1.5}{4-0}=\frac{1.5}{4}=0.375$.

Step5: Find the y - intercept $b$

From the point $(0,1.5)$, $b = 1.5$.
The equation of the line is $y = 0.375x+1.5$.

Answer:

For the first graph: $y=-0.875x + 3.5$; For the second graph: $y = 0.375x+1.5$