# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | January | Q#3

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**Question**

The line has equation 3x+5y-2=0.

**a. **Find the gradient of line for .

The line is perpendicular to and passes through the point (3,1).

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

**Solution**

**a.
**

We are given equation of the line as;

We are required to find the gradient of the line .

Slope-Intercept form of the equation of the line;

Where is the slope of the line.

Therefore, we can find slope of the line by rearranging its equation in terms slope-intercept form as follows.

Therefore, slope of the line is;

**b.
**

We are required to find equation of .

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 are given that line passes through the point (3,1) and is perpendicular to line .

If a line is normal to the curve , then product of their slopes and at that point (where line is normal to the curve) is;

Therefore;

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

From (a) we have found that;

Therefore;

Now we can write the equation of line .

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

Therefore;

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