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

Answer:

y - b = 1(x - a)  -  point-slope form

y = x + b - a  - slope-intercept form

Step-by-step explanation:

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

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

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

$m=\dfrac{b+3-b}{a+3-a}=\dfrac{3}{3}=1$

$y-b=1(x-a)$ - 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