# 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;          