Question

write a prediction line (equation of line of best fit) for the points in the table. be sure to graph the points so you can see the line of best fit.

x	2	4	6
y	7	13	19

hint: find the slope then use y - y1=m(x - x1) to write an equation.
show all work!
use the equation to predict the y value when x = 25.
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12pt paragraph

Explanation:

Step1: Calculate the slope (m)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(2,7)$ and $(x_2,y_2)=(4,13)$. Then $m=\frac{13 - 7}{4 - 2}=\frac{6}{2}=3$.

Step2: Use the point - slope form to find the equation

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(2,7)$ and $m = 3$, we have $y-7=3(x - 2)$.
Expand the right - hand side: $y-7=3x-6$.
Add 7 to both sides to get the slope - intercept form $y = 3x+1$.

Step3: Predict the y - value when x = 25

Substitute $x = 25$ into the equation $y=3x + 1$. Then $y=3\times25+1=75 + 1=76$.

Answer:

The equation of the line of best fit is $y = 3x+1$, and when $x = 25$, $y = 76$.