# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#4

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**Question**

The line has equation 4x + 2y – 3 = 0.

**a. **Find the gradient of .

The line is perpendicular to and passes through the point (2,5).

**b. **Find an equation of in the form y = mx + +c, where m and c are constants.

**Solution**

**a. **

We are given equation of line ;

We are required to find the gradient of .

Slope-Intercept form of the equation of the line;

Where is the slope of the line.

Therefore, we can rearrange the given equation of line in slope-intercept form, as follows, to find the gradient of the line.

Hence, gradient of the line is;

**b. **

We are required to find equation of line .

To find the equation of the line either we need coordinates of the two points on the line (Two-Point form of Equation of Line) or coordinates of one point on the line and slope of the line (Point-Slope form of Equation of Line).

We have coordinates of a point (2,5) on line but not slope of the line .

Next we need slope of the line to write its equation.

We are given that the line is perpendicular to .

If two lines are perpendicular (normal) to each other, then product of their slopes and is;

Therefore, if we have slope of line , we can find slope of the line .

From (a), we have found that , therefore;

With coordinates of a point on the line as B(2,5) and its slope

at hand, we can write equation of the line .

Point-Slope form of the equation of the line is;

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