Final answer:
To find the equation of a line that is parallel to the given line and passes through a point, we can use the point-slope form of a linear equation.
Step-by-step explanation:
To find an equation of a line that is parallel to the given line and passes through the point (6,-5), we need to use the fact that parallel lines have the same slope. The given line has a slope of 3, so the parallel line will also have a slope of 3. Using the point-slope form of a linear equation, we can write the equation as:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point. Substituting the values, we get:
y - (-5) = 3(x - 6)
y + 5 = 3x - 18
y = 3x - 23
So, the equation of the line that is parallel to the given line and passes through the point (6,-5) is
y = 3x - 23
.