We have that the equation represents a line in slope-intercept form:
[tex]y=mx+b\Rightarrow y=-4x+6[/tex]We have that m is the slope, in this case, m = -4, and 6 is the y-intercept (0, 6). The y-intercept is the point where the line passes through the y-axis - at this point x = 0.
Therefore, we still need another point to do the graph of the line. This point can be the x-intercept: the point where the line passes through the x-axis, and, at this point, y = 0. Then, to find it, we can proceed as follows:
y = 0
[tex]y=0\Rightarrow0=-4x+6[/tex]Subtracting 6 from both sides of the equation, we have:
[tex]-6=-4x+6-6\Rightarrow-6=-4x[/tex]Now, we can divide both sides of the equation by -4:
[tex]-\frac{6}{-4}=-\frac{4}{-4}x\Rightarrow x=\frac{6}{4}\Rightarrow x=\frac{3}{2}=1.5[/tex]Now, we have the y-intercept (0, 6) and the x-intercept (1.5, 0), and with these two points, we can graph the line. We need to remember that a line can be defined by two points.
