5. Write an equation in slope-intercept form for the line that is parallel to the given line and passes through the given point.
`y = 4x + 6`
and passes through (2, 7)
Since the line we need to find is parallel to the given line, it will have the same slope of 4.
The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
Using the point-slope form of a line y - y1 = m(x - x1), where (x1, y1) is the given point (2, 7), we can substitute the values into the equation:
y - 7 = 4(x - 2)
Simplifying,
y - 7 = 4x - 8
Finally, we can rewrite it in slope-intercept form by isolating y:
y = 4x - 8 + 7
y = 4x - 1
Therefore, the equation of the line parallel to y = 4x + 6 and passing through (2, 7) is y = 4x - 1.