Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | January | Q#3
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..
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;
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, if we have slope of line we can find slope of line .
From (a) we have found that;
Now we can write the equation of line .
Point-Slope form of the equation of the line is;