Question

Choose the point-slope form of the equation below that represents the line that passes through the point (6, −3) and has a slope of one half.

y − 6 = one half(x + 3)
y = one halfx − 6
y + 3 = one half(x − 6)
x − 2y = 12

Answer 1

`\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{-3})\qquad \qquad \qquad slope = m \implies \cfrac{1}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-3)=\cfrac{1}{2}(x-6)\implies y+3=\cfrac{1}{2}(x-6)`

Answer 2

Answer: y + 3 = one half(x − 6)

Explanation:

The equation of a line in point slope form with slope m and passing through point (a,b) is given by :-

`(y-b)=m(x-a)`

Given : The slope of the line :
`m=(1)/(2)`

The point from which line is passing : (a,b) = (6,-3)

Then , the point slope form of the given line will be :-

`(y-(-3))=(1)/(2)(x-6)\\\\\Rightarrow\(y+3)=(1)/(2)(x-6)`

Hence, the required equation is y + 3 = one half(x − 6)