Final answer:
The equation of the line that passes through the point (3,4) and is parallel to the line y = 3x − 2 is y = 3x − 5.
Step-by-step explanation:
The equation in slope-intercept form for a line that passes through the point (3,4) and is parallel to the line represented by y = 3x − 2 can be found by using the slope of the given line and the coordinates of the given point. Since the line we want is parallel to the given line, it will have the same slope, which is 3. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept for our new line, we plug in the coordinates of the given point (3,4) and the slope 3 to get 4 = 3(3) + b. Solving for b, we get b = -5. Therefore, the equation of the line is y = 3x − 5.