The equation of a line is \(2x-3y=6\). What is the slope of the line?
\(\dfrac{2}{3}\)
Given: the line \(2x-3y=6\), and we need its slope.
The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope.
Rearrange the equation to isolate \(y\): \(2x-3y=6\Rightarrow -3y=6-2x\).
Divide throughout by \(-3\): \(y=\dfrac{6-2x}{-3}=\dfrac{2x-6}{3}\).
This gives \(y=\dfrac{2}{3}x-2\), so the coefficient of \(x\) is the slope.
Therefore the slope \(m=\dfrac{2}{3}\).
Hence the slope of the line is \(\mathbf{\dfrac{2}{3}}\), i.e. 2/3.
Similar Questions
Which of the following equations represents a line parallel to \(3x - 2y = 6\)?
What is the x-intercept of the line given by \(2x-3y=12\)?
Find the equation of a line that is parallel to \(y=3x-5\) and passes through the point \((1,2)\).
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 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?
Find the equation of the line with slope -2 passing through the point (3, 5).
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 line passes through the point (5, 7) and has a slope of -1. What is the equation of the line?
If the graph of a linear equation passes through (0, -2) and has a slope -3, what is its equation?
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)?
In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
A1 (x1, y1), A2 (x2, y2), A3 (x3, y3) and A4 (x4, y4) are 4 points, p1 divides A1A2 in the ratio 1 ∶ 1, p2 divides P1A3 in the ratio 1 ∶ 2, P3 divides p2A4 in the ratio 1 ∶ 3. Then the coordinates of p3 are:
If (3, 2) are coordinates of the centroid of a triangle, whose vertices are (0, 4), (-2, 0) and (p, 2), then find the value of p.
