Would the equation of a line be incomplete without a definite y-intercept?

Question

Like on a test, if the directions mention \"the equation of a line,\" should I solve completely and have some definite values for the slope AND y-intercept, or would it be okay to leave it as y=2x+b? This probably seems like a really obvious question, but I just want to make sure.

Also, for the following problem, how would you determine what is what, as in what would be the slope and y-intercept?

} Find the slope-intercept form of the equation of the line passing through the points. Sketch a graph of the line.

} (-8, 1), (-8, 7)

I solved for the slope and it was undefined, and I know that the answer is x=-8 but I don\'t understand how or why that is...

Answer 1

 

Since x coordinates of the points are same, the line is a vertical line, and the line equation is x = -8.

Let\'s check the equation by solving the problem.

The line equation is y = mx + b

find the slope of the line m = (y2 - y1)/(x2 - x1) = (7 - 1) / (- 8 - (-8))

m = 6 / (-8+8) = 6 / 0 = undefined

The line equation is x = -8.

So, line is a vertical line.

Graph for the solutions is

Answer 2

 

Slope-intercept form straight line equation is y = mx + b

where m is slope and b is y - intercept.

Slope of the line m = rise / run

                              = difference of y - coordinates / difference of x - coordinates

                              = (y₂ - y₁) / (x₂ - x₁)

 

To solve the linear equation completely you must have any one of the folowing.

1. Any point on the line and slope.

or

2. Any two points on the line.

or

3. Intercepts of the line.

or

4.Slope and intercept.