Question

What is the equation for the line

Answer 1

y = - 2x - 4

Explanation:

the equation of a line in slope- intercept form is

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

To calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 4, 4) and (x₂, y₂ ) = (2, - 8) ← 2 points on the line

m =
`(-8-4)/(2+4)` =
`(-12)/(6)` = - 2

the line crosses the y-axis at (0, - 4) → c = - 4

y = - 2x - 4 ← equation of line

Answer 2

y= -2x-4

Explanation:

Since, from the graph,we can see it is a straight line, therefore we apply the equation of the straight line that is:

y= mx+c where m is the slope and c is the intercept.

Since the points are(-4,4) and (2,8),

m=
`(y_(2)-y_(1)  )/(x_(2)-x_(1)  )`

=
`(-8-4)/(2+4)`

=
`(-12)/(6)`

= -2

Therefore, m= -2

Now,since c is the intercept and the line cuts y- axis at (0,-4), therefore

c= -4

⇒y= mx +c

y= -2x+ (-4)

y= -2x_4