Question

Through : (-1,4) and (-4,2)

Answer 1

y - 4 = 2/3 (x + 1)

Step-by-step explanation:

The point-slope equation has the following form:

`y-y_0=m(x-x_0)`

Where (x0, y0) is a point and m is the slope of the line.

The slope can be calculated as:

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

Where (x1, y1) and (x2,y2) are two points in the line.

So, replacing (x1, y1) by (-1, 4) and (x2, y2) by (-4, 2), we get:

`m=(2-4)/(-4-(-1))=(-2)/(-4+1)=(-2)/(-3)=(2)/(3)`

Then, replacing m by 2/3 and (x0, y0) by (-1, 4), we get that the equation of the line is:

`\begin{gathered} y-4=(2)/(3)(x-(-1)) \\ y-4=(2)/(3)(x+1) \end{gathered}`

So, the answer is:

y - 4 = 2/3 (x + 1)