Final answer:
The equation of the line parallel to y = 2x - 6 that passes through the point (3, -8) is y = 2x - 14.
Step-by-step explanation:
The student is asking for the equation of a line parallel to a given line that passes through a specific point. A parallel line will have the same slope as the given line. Since the equation of the given line is y = 2x - 6, the slope (m) is 2. To find the equation of the parallel line, one can use the slope-intercept form of a line, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
To find the y-intercept (b) for the new line, we plug in the slope (2) and the coordinates of the point (3, -8) into the slope-intercept form equation and solve for b:
y = mx + b
-8 = 2(3) + b
-8 = 6 + b
b = -14.
So, the equation of the line parallel to y = 2x - 6 that passes through the point (3, -8) is y = 2x - 14.
To find the equation of the line parallel to y = 2x - 6 that passes through the point (3, -8), we need to determine the slope of the line first. Since the line we are looking for is parallel to y = 2x - 6, it will have the same slope of 2. Using the point-slope form of a linear equation, we can plug in the slope and the given point to find the equation.
Using the formula y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we have:
y - (-8) = 2(x - 3)
y + 8 = 2x - 6
Finally, rearranging the equation to the slope-intercept form y = mx + b, we get:
y = 2x - 14