Question

Graph the liney= -5x+2

Answer 1

To answer this question, we can find the intercepts of the line, since they are two points easy to identify on the coordinate plane. To find them, we can proceed as follows:

Finding the x-intercept

The x-intercept is the point where the line passes through the x-axis. At this point, y = 0. Then, we have:

$y=-5x+2\Rightarrow y=0\Rightarrow-5x+2=0$

Then, to solve the equation for x, we can subtract 2 from both sides of the equation, and then we have to divide both sides by -5 as follows:

$-5x+2-2=-2\Rightarrow-5x=-2\Rightarrow-\frac{5}{-5}x=-\frac{2}{-5}$$x=\frac{2}{5}=0.4$

Then, the x-intercept is (2/5, 0) or (0.4, 0). This is one point to graph the line.

Finding the y-intercept

The y-intercept is the point where the line passes through the y-axis. At this point, the value for x = 0. Then, we can proceed as follows:

$y=-5x+2\Rightarrow x=0\Rightarrow y=-5(0)+2\Rightarrow y=2$

Then, the y-intercept is (0, 2).

Graphing the line

We know that a line is defined by two points, and we have found two points for this line: (2/5, 0) and (0, 2). Then, we have:

We can appreciate that the line has a negative slope and that we have the two intercepts for the line (0, 2) and (0.4, 0).