Which of the following is the equation of a line parallel to the line y = 3x + 2, passing through the point (10,1)?
3x + y = 29
3x - y = 29
-3x - y = 29
3x + y = 29
recall the point-slope form of a line. In this case,
y-1 = 3(x-10)
Now massage that into one of the choices.
okay its definitely not C
idk why a and d are the same but that's what it shows on my paper, is it rather a and d?
No idea. But the answer is clearly B, if for no other reason than that x and y have opposite signs on the left.
okay, thank you.
To determine which equation represents a line parallel to y = 3x + 2 and passing through the point (10, 1), we need to understand the concept of parallel lines.
Parallel lines have the same slope. The given line, y = 3x + 2, has a slope of 3. Therefore, any line that is parallel to it must also have a slope of 3.
To find the equation of a line when given a point and the slope, we can use the point-slope formula:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line and m is the slope.
In this case, the point is (10, 1) and the slope is 3. We can substitute these values into the point-slope formula as follows:
y - 1 = 3(x - 10)
Distributing the 3 on the right side:
y - 1 = 3x - 30
Rearranging the equation to the standard form:
3x + y = 29
Therefore, the equation that represents a line parallel to y = 3x + 2 and passing through the point (10, 1) is 3x + y = 29.