Find the equation of the line drawn through the point of intersection of the lines x + y = 9 and 2x – 3y + 7 = 0 and whose slope is .
Suppose the given two lines intersect at a point P(x1, y1). Then, (x1, y1) satisfies each of the given equations.
x + y = 9 …(i)
2x – 3y + 7 = 0 …(ii)
Now, we find the point of intersection of eq. (i) and (ii)
Multiply the eq. (i) by 2, we get
2x + 2y = 18
or 2x + 2y – 18 = 0 …(iii)
On subtracting eq. (iii) from (ii), we get
2x – 3y + 7 – 2x – 2y + 18 = 0
⇒ -5y + 25 = 0
⇒ -5y = -25
⇒ y = 5
Putting the value of y in eq. (i), we get
x + 5 = 9
⇒ x = 9 – 5
⇒ x = 4
Hence, the point of intersection P(x1, y1) is (4, 5)
Now, we have to find the equation of the line passing through the point (4, 5) and having slope
Equation of line: y – y1 = m(x – x1)
⇒ 2x + 3y – 15 – 8 = 0
⇒ 2x + 3y – 23 = 0
Hence, the equation of line having slope -2/3 is 2x + 3y – 23 = 0