Question

Find equation of a line that contains the points 4 and -1, -1 and -4

Answer 1

You have to determine a line that crosses through the points (4,-1) and (-1,-4)

The first step is to determine the slope of the line, to do so you have to use the following formula:

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

Where

m is the slope

(x₁,y₁) are the coordinates to one point on the line

(x₂,y₂) are the coordinates to a second point on the line

`\begin{gathered} m=(-1-(-4))/(4-(-1)) \\ m=(-1+4)/(4+1) \\ m=(3)/(5) \end{gathered}`

The slope of the line that passes through (4,-1) and (-1,-4) is m = 3/5

Now that the slope is known, you can use the point-slope form to determine the equation.

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

Where

(x₁,y₁) are the coordinates of one point of the line

m is the slope

Replace the formula with the slope and one of the given points, for example (4,-1)

`\begin{gathered} y-(-1)=(3)/(5)(x-4) \\ y+1=(3)/(5)x-(3)/(5)\cdot4 \\ y+1=(3)/(5)x-(12)/(5) \end{gathered}`

Now you pass "1" to the right side to express the equation in slope-intercept form

`\begin{gathered} y+1-1=(3)/(5)x-(12)/(5)-1 \\ y=(3)/(5)x-(17)/(5) \end{gathered}`

The equation of the line that crosses the points (4,1) and (-1,-4) is

`y=(3)/(5)x-(17)/(5)`