Find the $y -$ intercept of the line passing through the points $A (3, - 2)$ and $B (- 1, 3)$ .

\frac{4}{7}

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\frac{7}{4}

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28

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11

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Solution

The correct option is B $\frac{7}{4}$
Using the two-point form, the equation of the line is
$\frac{y - y_{1}}{x - x_{1}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $\Rightarrow \frac{y - (- 2)}{x - 3} = \frac{3 - (- 2)}{- 1 - 3}$ $\frac{y - (- 2)}{x - 3} = \frac{5}{- 4}$
$- 4 y - 8 = 5 x - 15$
$5 x + 4 y - 7 = 0$
Now, we rearrange this equation into the slope-intercept form:
$4 y = - 5 x + 7$
$y = \frac{- 5}{4} x + \frac{7}{4}$
It is evident that the y-intercept is
$c = \frac{7}{4}$

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