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

Slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

Let the points are (x₁, y₁) = (- 8, 1) and (x₂, y₂) = (- 8, 7).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(7- 1)/(- 8 - (- 8))]

m  = [6/(- 8 + 8)]

⇒ m = 6/0 = undefined.

Now, the line equation is y = (6/0)x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (- 8, 1).

1 = (6/0)(- 8) + b

b = 1 + 48/0

⇒ b = 48/0 = undefined.

The line equation in slope - intercept - form is y = (6/0)x + (48/0).

Therefore, the line equation is x = - 8.

Graph :

1) Draw the coordinate plane.

2) Plot the points (- 8, 1), (- 8, 7), and (- 8, 0).

3) Connect the line through the plotted points.