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# when having a pair of solution such as (0,7) how do you graph this?

i can easily find the solutions for the ordered pair but i do no know how to graph them it always shows i am wrong when i try and that i need to lines?

### 2 Answers by Expert Tutors

Barbara B. | Experienced Math, Language, Test Prep Teacher Makes Tutoring a BreezeExperienced Math, Language, Test Prep Te...
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When you graph a line, it first depends on how the equation was written.

In slope-intercept form (y=mx+b), first graph the y-intercept (b) on the y-axis (the vertical one).  For example, if b is -5, then graph a point on the y-axis at (0, -5).  One thing to always remember:  at the y-intercept, is always equal to zero, or you wouldn't be intersecting the y-axis.  From that point, use the slope (m) to graph the next point.  Slope is a ratio of the change in the vertical or dependent variable to the horizontal or independent variable.  This may be your mistake; since we graph points horizontally and then vertically, it is often difficult to remember that slope is a ratio of vertical change over horizontal change.  For example, if your y-intercept is -5 and your slope is -2/3, from -5 go down 2 and to the right 3.  That will be a second point on your line, and you only need two points to define a line.  You can then draw the line with a ruler.  Do the same for the second line, and it should intersect at the solution if the slopes are different (see the last post).

In standard form, Ax + By = C, the easiest thing to do is substitute 0 in for x and solve for y.  That will give you one of your two points (0, y).  Then substitute 0 in for y.  That will give you a second point (x, 0). Again, use a ruler to draw your lines and find their intersection if there is a common solution to both equations.
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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to lines
^--------- to, too, or two (but not tutu)  ;)

When you say a solution is a point like (0,7) you're probably talking about the intersection of two graphs. Then that point can be substituted into the equation of either graph and the result will be a true statement.

If you are working with straight lines that have linear equations then:

a. if the lines intersect in one point then that is the only solution to the system of equations (the two describing the two lines);

b. if the equations describe the same graphed line (they're just algebraic manipulations of each other), then there are an infinite number of solutions: every point on the line; and

c. if the lines are parallel (same slope but different y-intercepts) then there are no solutions because there are no intersections.