The line \( y = 3x - 2 \) has a slope of 3. Find the equation of the line that is parallel to this line and passes through the point (2, -1).
Answer
Step3: Simplify the equation to get the standard form. It becomes \( y + 1 = 3x - 6 \). Further simplifying, we get \( y = 3x - 7 \).
Step 1 ：Step1: Recall that parallel lines have the same slope. So, the slope of the new line will also be 3.
Step 2 ：Step2: Use the point-slope form of a line, which is \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. Substituting the given point (2, -1) and the slope 3, we get \( y - (-1) = 3(x - 2) \).
Step 3 ：Step3: Simplify the equation to get the standard form. It becomes \( y + 1 = 3x - 6 \). Further simplifying, we get \( y = 3x - 7 \).
