jullysabat wrote:
Hello Bunnel,
Can you pls explain how did draw the graph...
How did you take the points of x and y..
\(y=mx+b\) is called
point-intercept form of equation of a line (in our case it's \(y=-\sqrt{3}*x-6\)), where \(m\) is the slope of the line; \(b\) is the y-intercept of the line; \(x\) is the independent variable of the function \(y\). To draw a graph of a line you need two points (any two distinct points (x,y) which satisfy the equation of a line) and then you just draw a line passing these points. Usually X and Y intercepts are best choices for the points.
X-intercept is
the point where a line (a graph) crosses the x-axis. So it's the point on x-axis, any point on x-axis has y-coordinate equal to zero, which means that X-intercept is the point \((x,0)\) - the value of \(x\) when \(y=0\): \(y=mx+b\) --> \(0=mx+b\) --> \(x=-\frac{b}{m}\). So X-intercept of a line \(y=mx+b\) is \(x=-\frac{b}{m}\);
Y-intercept is
the point where a line (a graph) crosses the y-axis. So it's the point on y-axis, any point on y-axis has x-coordinate equal to zero, which means that Y-intercept is the point \((0,y)\) - the value of \(y\) when \(x=0\): \(y=mx+b\) --> \(y=m*0+b\) --> \(y=b\). So Y-intercept of a line \(y=mx+b\) is \(y=b\).
In our case for the line given by \(y=-\sqrt{3}*x-6\):
X-intercept will be \((-2\sqrt{3}, \ 0)\), as x-intercept of a line is the value of x for y=0, the point where the line crosses X-axis: y=0 --> \(x=-2\sqrt{3}\);
Y-intercept will be \((0, \ -6)\), as y-intercept of a line is the value of y for x=0, the point where the line crosses Y-axis: x=0 --> \(y=-6\).
Check Coordinate Geometry chapter for more:
math-coordinate-geometry-87652.htmlHope it's clear.
Yeah its clear now...