KnowledgeBoat Logo

Mathematics

Find the equation of a line passing through the point (-2, 3) and having x-intercept 4 units.

Straight Line Eq

43 Likes

Answer

Since, x-intercept = 4, it means line will intersect x-axis at (4, 0).

Since, line passes through (-2, 3) and (4, 0) so by two-point formula, equation is,

y−y1=y2−y1x2−x1(x−x1)y - y1 = \dfrac{y2 - y1}{x2 - x1}(x - x1)

Putting values in above equation we get,

⇒y−3=0−34−(−2)(x−(−2))⇒y−3=−36(x+2)⇒y−3=−12(x+2)⇒2(y−3)=−x−2⇒2y−6=−x−2⇒2y+x−6+2=0⇒x+2y−4=0.\Rightarrow y - 3 = \dfrac{0 - 3}{4 - (-2)}(x - (-2)) \\[1em] \Rightarrow y - 3 = \dfrac{-3}{6}(x + 2) \\[1em] \Rightarrow y - 3 = \dfrac{-1}{2}(x + 2) \\[1em] \Rightarrow 2(y - 3) = -x - 2 \\[1em] \Rightarrow 2y - 6 = -x - 2 \\[1em] \Rightarrow 2y + x - 6 + 2 = 0 \\[1em] \Rightarrow x + 2y - 4 = 0.

Hence, the equation of the line is x + 2y - 4 = 0.

Answered By

17 Likes

Related Questions