Question

A line passes through the points (2,21) and (8,27). Write a linear function rule in terms of x and y for

Answer 1

We have two points so we can find the gradient using y1-y2/x1-x2
gradient = 21-27/2-8
= 1
we know the form for any linear equation is y = mx + c
we have m and a point so we can substitute in point (2,21) to find c
21 = 1 x 2 + c
c = 19
therefore, the equation is y = x + 19

Answer 2

Y = x + 19


Slope(m) formula: y2 - y1 / x2 - x1
y2 - y1 / x2 - x1 = 27 - 21 / 8 - 2 = 6 / 6 = 1

y = mx + b
y = 1x + b or y = x + b (the one is usually invisible)

Now, we use either one of our points to find b. I will be using (2, 21).

y = x + b
21 = 2 + b
- 2 - 2
19 = b

y = x + b -> y = x + 19


Check your answer using either one of the points.

y = x + 19
21 = 2 + 19
21 = 21
This statement is correct


y = x + 19
27 = 8 + 19
27 = 27
This statement is correct

Therefore, our equation is: y = x + 19



Hope this helps!