Answer:To find the equation of a line parallel to \(y = 3x - 2\) that passes through the point \((0, 5)\), we can use the fact that parallel lines have the same slope.
The slope of \(y = 3x - 2\) is \(m = 3\). So, the parallel line will also have a slope of \(m = 3\).
We now have the slope and a point \((0, 5)\). We can use the point-slope form of a linear equation:
\[y - y_1 = m(x - x_1)\]
Substituting \(m = 3\) and the point \((0, 5)\):
\[y - 5 = 3(x - 0)\]
Simplifying:
\[y - 5 = 3x\]
Now, you can express it in slope-intercept form:
\[y = 3x + 5\]
Explanation:
So, the equation of the line parallel to \(y = 3x - 2\) that passes through the point \((0, 5)\) is \(y = 3x + 5\).