Answer
$y=\frac{21}{32}x +\frac{33}{16}$
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:
$m=\dfrac{\frac{3}{4}-\frac{5}{2}}{-2-\frac{2}{3}}=\dfrac{-\frac{7}{4}}{-\frac{8}{3}}=\dfrac{-7}{4} \cdot \dfrac{-3}{8}=\dfrac{21}{32}$
Thus, the tentative equation of the line is $y=\frac{21}{32}x + b$.
Solve for the value of $b$ by substituting the x and y-coordinates of one point into the tentative equation to have:
$y=\frac{21}{32}x + b
\\\frac{3}{4} = \frac{21}{32} \cdot (-2)+b
\\\frac{3}{4}=-\frac{$21}{16}+b
\\\frac{3}{4}+\frac{21}{16}=b
\\\frac{33}{16}=b$
Therefore, the equation of the line in slope-intercept form is $y=\frac{21}{32}x +\frac{33}{16}$.
