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