Final answer:
To find the equation of the line parallel to y=3x+5 that passes through (-1, 2), we use the fact that parallel lines have the same slope. Thus, the new equation has the same slope, which is 3. After using the point (-1, 2) to solve for the y-intercept, the equation of the new line is y = 3x + 5.
Step-by-step explanation:
The question asks for the equation of a line that is parallel to a given line and that passes through a specific point. In slope-intercept form, the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Since parallel lines have the same slope, the slope of the new line will be the same as the given line, which is 3. Using the slope-point form (y - y1) = m(x - x1), with the point (-1, 2), we can substitute m = 3 and (x1, y1) = (-1, 2) to find the equation of the new line.
The calculation will be:
y - 2 = 3(x + 1)
Simplifying this, we get:
y - 2 = 3x + 3
y = 3x + 5
This gives us the new line's equation in slope-intercept form:
y = 3x + 5