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

+2 votes
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...
asked Dec 25, 2012 in ALGEBRA 2 by alg2trig Rookie
reshown Dec 28, 2012 by moderator

2 Answers

+2 votes

 

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

linear equation x = -8 graph

answered Dec 28, 2012 by steve Scholar
+2 votes

 

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)

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

 

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.

answered Dec 28, 2012 by steve Scholar

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