Question

Write the point-slope form of the equation of the line through the given points ( − 4, 1) and (4, 4)

Answer 1

The slope-point form:

`y=mx+b`

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (-4, 1) and (4, 4). Substitute:

`m=d(4-1)/(4-(-4))=(3)/(8)`

Therefore we have the equation of a line

`y=(3)/(8)x+b`

Put the coordinates of the point (4, 4) to the euation of a line:

`4=(3)/(8)(4)+b`

`4=(3)/(2)+b`

`4=1.5+b` subtract 1.5 from both sides

`2.5=b\to b=2.5\to b=(5)/(2)`

Answer:
`\boxed{y=(3)/(8)x+(5)/(2)}`