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:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]
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
[tex]\begin{gathered} m=\frac{-1-(-4)}{4-(-1)} \\ m=\frac{-1+4}{4+1} \\ m=\frac{3}{5} \end{gathered}[/tex]
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.
[tex]y-y_1=m(x-x_1)[/tex]
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)
[tex]\begin{gathered} y-(-1)=\frac{3}{5}(x-4) \\ y+1=\frac{3}{5}x-\frac{3}{5}\cdot4 \\ y+1=\frac{3}{5}x-\frac{12}{5} \end{gathered}[/tex]
Now you pass "1" to the right side to express the equation in slope-intercept form
[tex]\begin{gathered} y+1-1=\frac{3}{5}x-\frac{12}{5}-1 \\ y=\frac{3}{5}x-\frac{17}{5} \end{gathered}[/tex]
The equation of the line that crosses the points (4,1) and (-1,-4) is
[tex]y=\frac{3}{5}x-\frac{17}{5}[/tex]
