Answer:
[tex]y=2x-7[/tex]
Step-by-step explanation:
The equation for a straight line is
[tex]y=mx+c[/tex]
where m is the gradient and c is the y-intercept.
To have the full equation, we need to find m and c values.
To find m, the formula is
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
By substituting the two points (4,1) and (3,-1) into the formula, we get:
[tex]m =\frac{-1-1}{3-4} \\m=\frac{-2}{-1} \\m=2[/tex]
Now we have [tex]y=2x+c[/tex]
To solve for c, substitute any of the two points in to the equation. Let's say we insert (4,1) into the equation:
[tex]y=2x+c\\1=2(4)+c\\c=1-8\\c=-7[/tex]
Therefore, the full equation is
[tex]y=2x-7[/tex]
Pro tip:
You can always substitute (4,1) or (3,-1) to check if the equation is correct.
