本研究的主要目的是在於探討學生從從線型函數情境問題中建立關係式的解題策略及解題失敗原因。
研究方法是設計線型函數情境問題之診斷性問卷，以一個八年級班級的29位學生作為研究樣本，先進行問卷測驗，再藉由問卷作答內容作事後訪談，來探討學生處理線型函數情境問題的解題策略及解題失敗原因。
研究結果發現，
一、學生推論情境問題之變化率與起始值，以及計算情境特定值的解題策略可區分成操作圖形物件、比例推理與列聯立方程式。其中學生計算情境特定值的作法與推論變化率的作法較具有一致性。
二、學生建立關係式的解題策略可區分成類似遞迴想法、比例推理及列聯立方程式。學生理解變化率與起始值，能運用比例推理推算情境特定值，但是未必能理解變化率與起始值之代數表徵意義，將兩者轉換為線型函數關係式的參數。
三、解題失敗原因：
1.學生會因為誤解圖形資訊、不理解情境變化率與起始值的意義或誤解情境問題的描述，致使推論變化率與起始值時解題失敗。
2.學生會因為誤解圖形資訊、忽略起始值、變化率與起始值錯誤、關係式錯誤，情境與數量之間產生不適當的對應關係或引用錯誤數量關係等，致使計算情境特定值時解題失敗。
3.學生會因為忽略起始值、引用錯誤的變化率與起始值、情境與數量之間產生不適當的對應關係、或誤解文字符號的意義，致使建立錯誤關係式。
本研究所得到之學生建立線型函數關係式的解題策略及解題失敗原因等，可作為國中線型函數教學設計之參考。

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