Question 188244
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The <i>x</i>-intercept is the point (<i>a</i>,0).  So substitute 0 for <i>y</i> in your equation and calculate the value of the <i>x</i>-coordinate.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x + 0 = 5 \ \ \Rightarrow\ \ x = \frac{5}{3}]


Your 1.6 is probably close enough for this exercise, but you needed to put it in the correct place in the ordered pair describing the <i>x</i>-intercept, (1.6,0).


Now that you have two points, you can draw the boundary line.  Make it a solid line because the inequality included equals, i.e. it is *[tex \Large \leq] rather than <.


As to which side to shade, pick a point <i><b>not</b></i> on the boundary line.  If the line does not pass through the origin, the origin, (0,0) is always a good point to select.  Substitute the values of the coordinates of the selected point into your original inequality.  If the result is a true statement, then shade in the side of the line that contains the point.  If the result is a false statement, shade in the other side.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3(0) + 0 \leq 5]


Is a true statement, so the side of the line containing the point (0,0) is the side that gets the shading.  In this case, that would be below and to the left.


{{{drawing(
500, 500, -5, 5, -5, 5,
grid(1),
red(locate(-3,1,This),
locate(-3,.7,side),
locate(-3,.4,gets),
locate(-3,-.3,the),
locate(-3,-.6,shading)),
graph(
500, 500, -5, 5, -5, 5,
-3x+5
))}}}

John
*[tex \LARGE e^{i\pi} + 1 = 0]
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