If 3x + y = 5 and 6x + ay = 7 are intersecting lines, then find the value of a.If 3x + y = 5 and 6x + ay = 7 are intersecting lines, then find the value of a.
Answers
Equation of a line whose slope and y-intercept is given by:
y = mx + c, where m is the slope and c is the y-intercept
(i) Given: slope = 3, y-intercept = – 5
⇒ y = 3x + (-5)
Hence, the equation of line is y = 3x – 5.
(ii) Given: slope = -2/7, y-intercept = 3
⇒ y = (-2/7)x + 3
y = (-2x + 21)/7
7y = -2x + 21
Hence, the equation of line is 2x + 7y – 21= 0.
(iii) Given: gradient = √3, y-intercept = -4/3
⇒ y = √3x + (-4/3)
y = (3√3x – 4)/3
3y = 3√3x – 4
Hence, the equation of line is 3√3x – 3y – 4 = 0.
(iv) Given: inclination = 30°, y-intercept = 2
Slope = tan 30o = 1/√3
⇒ y = (1/√3)x + 2
y = (x + 2√3)/ √3
√3y = x + 2√3
Hence, the equation of line is x – √3y + 2√3 = 0.
Equation of a line whose slope and y-intercept is given by:
y = mx + c, where m is the slope and c is the y-intercept
(i) Given: slope = 3, y-intercept = – 5
⇒ y = 3x + (-5)
Hence, the equation of line is y = 3x – 5.
(ii) Given: slope = -2/7, y-intercept = 3
⇒ y = (-2/7)x + 3
y = (-2x + 21)/7
7y = -2x + 21
Hence, the equation of line is 2x + 7y – 21= 0.
(iii) Given: gradient = √3, y-intercept = -4/3
⇒ y = √3x + (-4/3)
y = (3√3x – 4)/3
3y = 3√3x – 4
Hence, the equation of line is 3√3x – 3y – 4 = 0.
(iv) Given: inclination = 30°, y-intercept = 2
Slope = tan 30o = 1/√3
⇒ y = (1/√3)x + 2
y = (x + 2√3)/ √3
√3y = x + 2√3
Hence, the equation of line is x – √3y + 2√3 = 0.