Answer
$y=-5x+11$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b = y-intercept.
(2) The slope of a line can be found using the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line.
Solve for the slope to obtain:
$m=\dfrac{6-1}{1-2}
\\m=\dfrac{5}{-1}
\\m=-5$
Thus, the tentative equation of the line is:
$y=-5x+b$
To find the value of $b$, substitute the coordinates of $(2, 1)$ into the tentative equation above to obtain:
$y=-5x+b
\\1 = -5(2)+ b
\\1 = -10 + b
\\1+10= b
\\11=b$
Therefore, the equation of the line is:
$y=-5x+11$
