Answer:
y = 2x + 3
Step-by-step explanation:
The equations appear to be in y intercept form: y = mx + b
Where m = slope and b = y intercept.
In order to write an equation we must identify the slope and y intercept. The slope can be found using the formula [tex]\frac{y_2-y1}{x_2-x_1}[/tex] where (x1 , y1 ) and ( x2 , y2 ) are derived from any points in the table or graph.
Note that it does not matter which two points are chosen, choosing any two would result in the same answer.
The two points I chose were (0,3) and (1,5)
To find the slope we simply plug in the x and y values into the slope formula
[tex]\frac{y_2-y1}{x_2-x_1}[/tex]
(x1,y1) ---> (0,3) ----> x1 = 0 and y1 = 3
(x2,y2) ---> (1,5) ----> x2 = 1 and y2 = 5
- plug in values into formula -
[tex]\frac{5-3}{1-0}[/tex]
subtract 3 from 5 and 0 from 1
[tex]\frac{5-3=2}{1-0=1} =\frac{2}{1}[/tex]
simplify fraction
slope = 2
We now need to find the y intercept. The y intercept is the value of y when x = 0. Thankfully the value of y when x = 0 is given to us. The y intercept is 3
We then plug in the slope and y intercept into slope intercept form
y = mx + b
slope (m) = 2
y intercept (b) = 3
y = 2x + 3
And we are done!
