<span>4. x = first integer </span> <span>x + 2 = 2nd integer </span> <span>x + x + 2 = 80 -- combine like terms </span> <span>2x + 2 = 80 -- subtract 2 from both sides </span> <span>2x = 80 - 2 </span> <span>2x = 78 -- divide both sides by 2 </span> <span>x = 39 <== this is the smallest number </span> <span>x + 2 = 41 </span>
<span>5. p = 1/2g - 3 </span>
<span>6. The union of two sets is all the numbers in both sets, no need to copy the same number more then once. Answer is : (1,2,3,4,5,6,8,10) </span>
<span>7. 2x + 3y <= 6 -- put in y = mx + b form </span> <span>3y <= -2x + 6 </span> <span>y <= -2/3x + 2 </span> <span>In y = mx + b form, the y intercept is in the b position. So the y intercept is (0,2) </span> <span>To find the x intercept, sub in 0 for y (change inequality sign to equal sign) </span> <span>2x + 3y = 6 </span> <span>2x + 3(0) = 6 </span> <span>2x = 6 </span> <span>x = 3 </span> <span>x intercept is (3,0) </span> <span>So plot your points (3,0) and (0,2) </span> <span>Connect the points with a solid line because there is an equal sign in there. </span> <span>Shade below the line because it is less then. </span>
<span>Perpendicular lines have negative reciprocal slope. All that means is " flip " the slope and change the sign. The slope in these equations are -1/2 and 2. These are negative reciprocals of each other. </span>
<span>y = mx + b </span> <span>(0,6) x = 0 and y = 6 </span> <span>6 = 0(-2) + b </span> <span>6 = b </span>
<span>your equation is : y = -2x + 6 (slope intercept form) </span> <span>2x + y = 6 (standard form) </span>
<span>11. x + y = 5 -- put this in y = mx + b form, and the m position is your slope </span> <span>y = -x + 5 (-x is the same as -1x) so your slope is -1 </span>
<span>12. 4y = 8x - 3 -- put in y = mx + b form, and the b stands for the y intercept </span> <span>y = 8/4x - 3/4 </span> <span>y = 2x - 3/4 (the y intercept is -3/4 </span>
<span>13. |a| + b --- (a = -1.4 and b = -2.7) </span> <span>absolute values, whether they have a negative or not, they are always positive </span> <span>|a| + b </span> <span>|-1.4 | + (-2.7) </span> <span>1.4 - 2.7 = -1.3 <== your answer </span>
<span>14. I cannot see the problem </span>
<span>15. -4 < 2t <= 2 --- divide everything by 2 </span> <span>-2 < t <= 1 </span> <span>open circle on -2, closed circle on 1, shading in between </span>
<span>16. x + 2y = -9 ---> x = -2y - 9 </span> <span>now sub -2y - 9 in for x in the other equation </span> <span>4x - 2y = 14 </span> <span>4(-2y - 9) - 2y = 14 -- distribute through the parenthesis </span> <span>-8y - 36 - 2y = 14 -- add 36 to both sides </span> <span>-8y - 2y = 14 + 36 combine like terms </span> <span>-10y = 50 -- divide by -10 </span> <span>y = -5 </span> <span>now sub -5 in for y in either of the original equations </span> <span>x + 2y = -9 </span> <span>x + 2(-5) = -9 </span> <span>x - 10 = -9 </span> <span>x = -9 + 10 </span> <span>x = 1 </span> <span>answer : x = 1 and y = -5 or (1,-5) </span>
<span>I was really bored so I thought I would just help out :)</span>
I will be glad to help you in the comments. I do need to know though, what is the class this is presented in? Is this algebra, or calculus? Depending on the class, we have different approaches.
An undefined slope would look like a vertical line, up and down. This is shown using an x equals equation instead of a y equals equation.
Since the line goes vertically, you only need to look at the x-value to make the equation, since after doing x = -4 the line would keep going down until it touched (-4, -8).
The line would touch everything in the y-value but stay at x = -4.
Therefore the answer to this problem is x = -4. I've attached a picture (from desmos) showing what the graph of x = -4 would look like and how it touches the point (-4, -8).
