Find the slope and y-intercept of the lines $3 x - 4 y = 5$ .

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Solution

We solve the given line $3 x - 4 y = 5$ for $y$ as follows:

$3 x - 4 y = 5 \Rightarrow 4 y = 3 x - 5 \Rightarrow y = \frac{3 x - 5}{4} \Rightarrow y = \frac{3}{4} x + (- \frac{5}{4}) . . . . . . (1)$

We know that the equation of a line is $y = m x + c$ where $m$ is the slope of the line and $c$ is the y-intercept.

Comparing the equation of line $y = m x + c$ with equation 1 we have,

$m = \frac{3}{4}$ and $c = - \frac{5}{4}$

Hence, the slope of the line is $\frac{3}{4}$ and the y-intercept is $- \frac{5}{4}$ .

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