To find an equation for a line that is parallel to the given line, we need to consider that parallel lines have the same slope. The given line has a slope of 3 (from the equation y=3x+4). Now, let's use the point-slope form of a linear equation to find the equation for the line that passes through the given point (6,8).
The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line. Plugging in the values, we get:
y - 8 = 3(x - 6)
Simplifying the equation, we have:
y - 8 = 3x - 18
Adding 8 to both sides, we have:
y = 3x - 10
Therefore, the equation for the line that is parallel to y=3x+4 and passes through (6,8) is y=3x-10.
So the correct answer is A. y=3x-10.
To determine whether the lines for each pair of equations are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of an equation (y=mx+b) allows us to easily see the slope.
For the first pair of equations:
Given: y = -3x + 7
Comparing with y = mx + b, we find that the slope is -3.
For the second equation: -2x + 6y = 3
We need to rearrange the equation to slope-intercept form:
6y = 2x + 3
y = 2/6x + 3/6
y = 1/3x + 1/2
Comparing with y = mx + b, we find that the slope is 1/3.
Since the slopes are not the same (i.e. -3 and 1/3 are not equal), the lines for the pair of equations are neither parallel nor perpendicular.
So the correct answer is C. Neither.
Therefore, the correct answers are:
1. B. y=3x-10
2. C. Neither