Question

How do I graph y = -4x + 6 thanks!

Answer 1

We have that the equation represents a line in slope-intercept form:

`y=mx+b\Rightarrow y=-4x+6`

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

`y=0\Rightarrow0=-4x+6`

Subtracting 6 from both sides of the equation, we have:

`-6=-4x+6-6\Rightarrow-6=-4x`

Now, we can divide both sides of the equation by -4:

`-(6)/(-4)=-(4)/(-4)x\Rightarrow x=(6)/(4)\Rightarrow x=(3)/(2)=1.5`

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.