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Find the gradient of the line with equation $2x + 5y = 7$ - AQA - A-Level Maths Mechanics - Question 1 - 2017 - Paper 1

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Question 1

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Find the gradient of the line with equation $2x + 5y = 7$. Circle your answer.

Worked Solution & Example Answer:Find the gradient of the line with equation $2x + 5y = 7$ - AQA - A-Level Maths Mechanics - Question 1 - 2017 - Paper 1

Step 1

Step 1: Rearrange the Equation

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Answer

To find the gradient of the line, we first need to rearrange the equation into the slope-intercept form, which is y=mx+cy = mx + c, where mm is the gradient. Starting with the equation:

2x+5y=72x + 5y = 7

We can isolate yy:

5y=7−2x5y = 7 - 2x y=−25x+75y = -\frac{2}{5}x + \frac{7}{5}

Step 2

Step 2: Identify the Gradient

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Answer

From the rearranged equation y=−25x+75y = -\frac{2}{5}x + \frac{7}{5}, the coefficient of xx (which is mm) represents the gradient. Thus, the gradient of the line is:

m=−25m = -\frac{2}{5}

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