What equation does Karissa get if she found the equation of the line passing through the point (2,1) that is parallel to the line with equation y=3x+4

Answer 1

A parallel line will have have the same slope of 3 (y = mx + b, where m is the slope and b is the y-int.)

So we need to find b for the new line. It goes through point (2,1) so we can substitute those values for x and y and solve for b.

1 = 3(2) + b, so b = -5

y = 3x - 5

Answer 2

These types of questions rely on understanding what it means to be "parallel" as well as how to find the slope in an equation. First, remember that parallel just means that two lines will never meet because their slopes are equal. Thus, we need to find the slope of the given line equation.

To do that, we look at the slope-intercept formula y=mx + b where m is the slope and b is the intercept. Well, in the given equation, we see that y=3x+4, thus m=3 (our slope is 3). A parallel line must have a slope of 3.

The only thing left to figure out is the intercept of the parallel line (b in the y=mx+b equation). To do this, we take the information given (that the line goes through 2,1 and is parallel to the line with slope=3) and plug it into the slope-intercept formula. We do this because we know that at the point where x=2, y must equal 1. We also know that the line has the slope of 3. Thus, there's only 1 line that fits all of those parameters. We just need to figure out where it crosses the y=axis.

So let's plug values in:

y=mx+b (use x=2, y=1, and m=3... solve for b)

1 = 3(2) + b

1 = 6 + b

b = -5

So your formula then becomes y = mx + b using the m and b values that you found (m=3, b=-5).

y=3x-5