What is the x-intercept of the line given by \(2x-3y=12\)?
6
The x-intercept of a straight line is the point where the line crosses the x-axis, and every point on the x-axis has a y-coordinate of zero.
So to find the x-intercept, set \(y = 0\) in the equation of the line.
The line is \(2x - 3y = 12\); putting \(y = 0\) gives \(2x - 3(0) = 12\).
This simplifies to \(2x = 12\).
Dividing both sides by 2: \(x = \dfrac{12}{2} = 6\).
So the line meets the x-axis at the point \((6, 0)\), and the x-intercept is the value 6.
Key concept: x-intercept is found by substituting \(y = 0\); a y-intercept would instead need \(x = 0\).
The x-intercept is 6.
Similar Questions
Which of the following equations represents a line parallel to \(3x - 2y = 6\)?
Find the equation of a line that is parallel to \(y=3x-5\) and passes through the point \((1,2)\).
The coordinates of the vertices of a triangle are \(A(0,0),\ B(8,0),\) and \(C(0,6)\). What is the location of the orthocenter?
A drone flies along \(y = -x + 10\). Another follows \(y = x - 4\). At what point do they intersect?
A land plot is defined by points A(0,0), B(4,0), C(5,3), D(1,3). What is the area of the parallelogram representing this plot?
The equation of a line is \(2x-3y=6\). What is the slope of the line?
Find the equation of the line with slope -2 passing through the point (3, 5).
A triangle has vertices with coordinates A(1,2), B(5,2), and C(3,8). What is the y-coordinate of its centroid?
A line passes through the point (5, 7) and has a slope of -1. What is the equation of the line?
Important Questions from Co-ordinate Geometry
In which ratio the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3)?
The area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:
In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
Find the value of K for which equation x – Ky = 2, 3x + 2y = 5 has unique solution.
