Final answer:
The equation of the line that is parallel to y=3x+5 and passes through the point (-4, -13) is y = 3x - 1. This is based on the fact that parallel lines have equal slopes and using the point-slope form of the equation of a line.
Step-by-step explanation:
To write an equation that is parallel to y=3x+5 and passes through the point (-4, -13), we need to understand the concept of parallel lines in the coordinate plane. Two lines are parallel if and only if their slopes are equal. In the equation y=3x+5, the slope (m) is 3. Therefore, any line that is parallel to it will also have a slope of 3.
Next, we use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. For our case:
- The slope m is 3 (same as the given line).
- The point (x1, y1) is (-4, -13).
Substituting these values into the point-slope form, we get:
y - (-13) = 3(x - (-4))
y + 13 = 3(x + 4)
Expanding and simplifying:
y = 3x + 12 - 13
y = 3x - 1
So, the equation of the line that is parallel to y = 3x + 5 and passes through (-4, -13) is y = 3x - 1.