#### Answer

$y=6x -3.5$.

#### Work Step by Step

RECALL:
(i)
The slope-intercept form of a line's equation is $y=mx+b$ where $m$ = slope and $b$ = y-intercept.
(ii) The formula for slope is $m=\dfrac{y_2-y_1}{x_2-x_1}$.
Solve for the slope using the formula above to have:
$m=\dfrac{-2-\frac{1}{2}}{\frac{1}{4}-\frac{2}{3}}=\dfrac{-\frac{5}{2}}{-\frac{5}{12}}=\dfrac{-5}{2} \cdot \dfrac{-12}{5}=6$
Thus, the tentative equation of the line is $y=6x + b$.
Solve for the value of $b$ by substituting the x and y-coordinates of one point into the tentative equation to have:
$y=6x+b
\\-2 = 6(\frac{1}{4})+b
\\-2=1.5+b
\\-2-1.5=b
\\-3.5=b$
Therefore, the equation of the line in slope-intercept form is $y=6x -3.5$.