A line passes through
(2, -1) and (4, 5)
We can say, given:
[tex]\begin{gathered} (x_1,y_1)=(2,-1) \\ \text{and} \\ (x_2,y_2)=(4,5) \end{gathered}[/tex]The equation of a line is given as:
[tex]y=mx+b[/tex]Where
m is slope and b is y-intercept
Now, finding the slope using the slope formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{5+1}{4-2} \\ m=\frac{6}{2} \\ m=3 \end{gathered}[/tex]So, the equation becomes:
y = 3x + b
Putting a point in (x,y), such as (4,5), we have:
y = 3x + b
5 = 3(4) + b
5 = 12 + b
b = 5 - 12
b = -7
Thus,
equation of the line >>> y = 3x - 7
Re-arranging in standard form >>> -3x + y = -7
Last Answer choice is right.
