Find the equation of the line parallel to the line \(3x - 4y = 12\) and passing through the point \((2, -3)\).
Answer
Step 4: Substitute the slope and y-intercept into the equation \(y = mx + b\) to find the equation of the line. We get \(y = \frac{3}{4}x - \frac{9}{2}\).
Step 1 ：Step 1: Find the slope of the given line. We know the general form of a linear equation is \(y = mx + b\), where \(m\) is the slope. So we need to convert the given equation into this form. We have \(3x - 4y = 12\), so \(y = \frac{3}{4}x - 3\). Hence, the slope of the given line is \(\frac{3}{4}\).
Step 2 ：Step 2: Since the line we are looking for is parallel to the given line, it will have the same slope, that is, \(m = \frac{3}{4}\).
Step 3 ：Step 3: Substitute the slope and the given point \((2, -3)\) into the equation \(y = mx + b\) to find the y-intercept \(b\). We get \(-3 = \frac{3}{4} * 2 + b\), which simplifies to \(-3 = \frac{3}{2} + b\). Solving for \(b\), we get \(b = -3 - \frac{3}{2} = -\frac{9}{2}\).
Step 4 ：Step 4: Substitute the slope and y-intercept into the equation \(y = mx + b\) to find the equation of the line. We get \(y = \frac{3}{4}x - \frac{9}{2}\).
