Question

The y-intercept of the line 5x - 8y = -2 is

Answer 1

$= > 5x - 8y = - 2 \\ = > 5x + 2 = 8y \\ = > y \: \: \: \: \: \: \: \: \: \: = \frac{5x + 2}{8} \\ \\ when \: x \: = 0 \\ = > y = \frac{5 \times 0 + 2}{8} \\ = > y = \frac{2}{8} \\ = > y = \frac{1}{4}$

therefore y - intercept is 1/4

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

The general equation of any line is

$ax + by + c = 0$

Which can be rewritten as

$y = mx + k$

Where m = slope of the line

k = y - intercept

$\blacksquare \:$CALCULATION

The given equation of the line is

$5x - 8y = -2$

Which can be rewritten as

$\displaystyle \: y \: = \frac{5}{8} x + \frac{2}{8}$

$\implies \: \displaystyle \: y \: = \frac{5}{8} x + \frac{1}{4}$

So the y - intercept is $\displaystyle \: \frac{1}{4}$