Question

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

• A. $\frac{4}{7}$
• B. $\frac{7}{4}$
• C. $28$
• D. $11$

Answer 1

The correct option is B $\frac{7}{4}$

Using the two-point form, the equation of the line is
$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$ $\Rightarrow \frac{y-(-2)}{x-3}=\frac{3-(-2)}{-1-3}$ $\frac{y-(-2)}{x-3}=\frac{5}{-4}$
$-4y-8=5x-15$
$5x+4y-7=0$
Now, we rearrange this equation into the slope-intercept form:
$4y=-5x+7$
$y=\frac{-5}{4}x+\frac{7}{4}$
It is evident that the y-intercept is
$c=\frac{7}{4}$