Question

How do i solve and graph -2x+5y=14

Answer 1

Explanation:

We assume you want to "solve" for some points that are on the graph.

You can observe that the constant (14) is a multiple of the x-coefficient (-2), so it will be convenient to solve for the x-intercept. Set y=0 and solve for x:

  -2x = 14

  x = -7 . . . . divide by -2

This tells you that (-7, 0) is a point on the graph.

To find another point on the graph with integer coordinates, you can change y by the opposite of the amount of the x-coefficient, or vice versa. Let's change y by +2 from 0 to 2, then we have ...

  -2x +5·2 = 14

  -2x = 4 . . . . . . subtract 10

  x = -2 . . . . . . . divide by -2

This tells you that (-2, 2) is another point on the graph.

The graph of the equation will be the line through these two points.

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You can find points on the line any of several ways. One way is to divide this equation by the constant on the right and rearrange so the coefficients are denominators:

  x(-2/14) + y(5/14) = 1

  x/(-7) + y/(2.8) = 1

These denominators are the respective intercepts, so you know immediately that points (-7, 0) and (0, 2.8) are on the line.

We did this mentally and realized that the y-intercept is not easy to graph. Hence the procedure above was used to find points with integer coordinates.