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?

Accepted Solution

Answer:y - b = 1(x - a)  -  point-slope formy = x + b - a  - slope-intercept formStep-by-step explanation:The point-slope form of an equation of a line:[tex]y-y_1=m(x-x_1)[/tex]The formula of a slope:[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]We have the points (a, b) and (a + 3, b + 3). Substitute:[tex]m=\dfrac{b+3-b}{a+3-a}=\dfrac{3}{3}=1[/tex][tex]y-b=1(x-a)[/tex] - point-slope formConvert to the slope-intercept form: y = mx + b:[tex]y-b=x-a[/tex]        add b to both sides[tex]y=x+b-a[/tex] - slope-intercept form