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The X axis represents temperature, while the Y axis represents heat. The slated lines represent the water at a set phase, increasing in temperature. As heat is supplied, the slope increases and the temperature of water rises, but the phase does not change. The straight lines represent water going through a phase change. As heat is supplied, the temperature stays the same, so the heat is going toward supplying the energy required in changing the phase of water rather than raising the temperature.
The slanted lines show and include all temperatures where only one state exists (ex. solid, liquid, gas). While the straight lines show melting/vaporization. Therefore, at that temperature, both phases that it is in between are present. Think about when ice is melting. It does not immediately go from solid to liquid. It melts slowly so there is a mix of both states. On the flat lines, at that temperature, the graph is indicating that both phases could be present.
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