Find the equation of the straight line that has y-intercept 4 and is parallel to the straight line 2x - 3y = 7

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Solution

Given line is 2x - 3y = 7
(1) $\Rightarrow$ 3y = 2x - 7 $\Rightarrow$ y = $\frac{2}{3} x - \frac{7}{3}$
$∴$ Slope of (1) is 2/3. The required line is parallel to (1) so its slope is also 2/3 y-intercept of required line = 4
$∴$ By using y = mx + c form the equation of the required line is y = $\frac{2}{3} x + 4 o r 2 x - 3 y + 12 = 0$

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