Answer:To find the equation of a line that is parallel to a given line, we need to determine the slope of the given line and then use that slope to write the equation of the parallel line.
For #2: (6,4) and the line equation 2x + 3y = 18
1) First, let's rewrite the given equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
2x + 3y = 18
3y = -2x + 18
y = (-2/3)x + 6
2) The given line has a slope of -2/3. Since we want to find a line parallel to it, the parallel line will have the same slope of -2/3.
3) Now, we can use the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the given point and m is the slope.
Using the point (6,4) and the slope -2/3, we have:
y - 4 = (-2/3)(x - 6)
4) Simplifying the equation, we can distribute -2/3 to (x - 6):
y - 4 = (-2/3)x + 4
5) Finally, let's rewrite the equation in slope-intercept form:
y = (-2/3)x + 8
Therefore, the equation of the line that passes through the point (6,4) and is parallel to the line 2x + 3y = 18 is y = (-2/3)x + 8.
Step-by-step explanation:
