Question

Find the equation of the line shown.

y
10
9
876
5
4
3
2
1
O
1 2 3 4 5 6 7 8 9 10
X

Answer 1

Answer: y=1x+6

Explanation:

The equation of a line is y=mx+c

m is the gradient and c is the y intercept.

on the graph the line intercepts the y axis at 6- the y intercept!

The gradient is the difference in y divide by the difference in x.

(0,6) and (4,10)

10-6=4

4-0=

4

4/4 is 1! so the equation is

y=1x+6

Answer 2

y = x + 6

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (4, 10) ← 2 points on the line

m =
`(10-6)/(4-0)` =
`(4)/(4)` = 1

the line crosses the y- axis at (0, 6 ) ⇒ c = 6

y = x + 6 ← equation of line