Question

What is the equation of the line which passes through (-0.5,-5) and (2,5)

Answer 1

Gradient (m) = x2-x1

y2-y1

considering

y1 = -5 y2 = 5

x1 = -0.5. x2 = 2

m = 2-(-0.5)

5-(-5)

m = 5.5

10

m = 11. = 0.55

20

equation of a line is given by

y-y1 = m+(x-x1)

y-(-5) =0.55 + {x-(-0.5)}

y+5 = 0.55 + x+0.5

making y the subject

y = 0.55 +0.5 -5 + x

y = -3.95 + x

Answer 2

`y = 4x-3`

Explanation:

The coordinates are (-0.5,-5) and (2,5)

Finding the slope, m:

=> Slope =
`(rise)/(run)`

=> Slope =
`(5+5)/(2+0.5)`

=> Slope =
`(10)/(2.5)`

=> Slope = 4

Now, y-intercept, b:

Taking any of the two coordinate and putting it in the slope intercept equation:

=> Point = (x,y) = (2,5)

So, x = 2, y = 5

=>
`y = mx+b`

=> 5 = (4)(2) + b

=> 5 = 8 + b

=> b = 5-8

=> b = -3

Now, Putting in slope intercept equation:

=>
`y = mx+b`

=>
`y = 4x-3`