Question

A line contains the points (a,b) and (a+3,b+3). Find the equation of the line in terms of a and b in point slope form and then convert it to slope intercept form?

Answer 1

Explanation:

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Answer 2

y - b = 1(x - a) - point-slope form

y = x + b - a - slope-intercept form

Explanation:

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)`

The formula of a slope:

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

We have the points (a, b) and (a + 3, b + 3). Substitute:

`m=(b+3-b)/(a+3-a)=(3)/(3)=1`

`y-b=1(x-a)` - point-slope form

Convert to the slope-intercept form: y = mx + b:

`y-b=x-a` add b to both sides

`y=x+b-a` - slope-intercept form