Problem: Write an article based on this summary: Define slope. Visualize a line’s “rise over run. Locate the slope of a line in an equation. Assess the steepness of the line. Identify a positive slope. Identify a negative slope. Understand the slope of a horizontal line. Understand the slope of a vertical line.

Answer: The slope is a measure of how steep a straight line is.  A variety of branches of mathematics use slope. In geometry, you can use the slope to plot points on a line, including lines that define the shape of a polygon. Statisticians use slope to describe the correlation between two variables. Economists use slope to show and predict rates of change.  People also use slope in real, concrete ways. For example, slope is used when constructing roads, stairs, ramps, and roofs. ” The term “rise” refers to the vertical distance between two points, or the change in y{\displaystyle y}. The term “run” refers to the horizontal distance between two points, or the change in x{\displaystyle x}. When learning about the slope of a line, you will often see the formula slope=riserun{\displaystyle {\text{slope}}\;={\frac {\text{rise}}{\text{run}}}} For example a slope of a line might be 21{\displaystyle {\frac {2}{1}}}. This means that to go from one point to the next, you need to go up 2 along the y-axis, and over 1 along the x-axis. You can do this using the slope-intercept form of a line’s equation. The slope-intercept form says that y=mx+b{\displaystyle y=mx+b}. In this formula, m{\displaystyle m} equals the slope of the line. You can rearrange the equation of a line into this formula to find the slope. For example, in the equation y=3x+1{\displaystyle y=3x+1}, the slope would be 3{\displaystyle 3}. You can still think of this slope in terms of rise over run if you turn it into a fraction. Any whole number can be turned into a fraction by placing it over 1. So, 3=31{\displaystyle 3={\frac {3}{1}}}. This means that the line represented by this equation rises 3 units vertically for every 1 unit it runs horizontally. The larger the slope, the steeper the line. A line is steeper the more vertical it rests on a coordinate plane. For example, a slope of 2 (that is, 21{\displaystyle {\frac {2}{1}}}) is steeper than a slope of 0.5 (12{\displaystyle {\frac {1}{2}}}). A positive slope is one that moves up and to the right. In other words, in a positive slope, as x{\displaystyle x} increases, y{\displaystyle y} also increases.  A positive slope is denoted by a positive number. A negative slope is one that moves down and to the right. In other words, in a negative slope, as x{\displaystyle x} increases, y{\displaystyle y} decreases.  A negative slope is denoted by a negative number, or a fraction with a negative numerator. To help remember the difference between a positive and negative slope, you can think of yourself as standing on the left endpoint of the line. If you need to walk up the line, it’s positive. If you need to walk down the line, it’s negative.  Knowing the difference between negative and positive slopes can help you check that your calculations are reasonable. A horizontal line is a line that runs straight across a coordinate plane. The slope of a horizontal line is 0. This makes sense if you think of lines in terms of slope=riserun{\displaystyle {\text{slope}}\;={\frac {\text{rise}}{\text{run}}}}. For a horizontal line, the rise is 0, since the y{\displaystyle y} value never increases or decreases. So, the slope of a horizontal line would be 0x{\displaystyle {\frac {0}{x}}}. The slope of a vertical line is undefined. In terms of riserun{\displaystyle {\frac {\text{rise}}{\text{run}}}}, the slope of a negative line would be y0{\displaystyle {\frac {y}{0}}}. The run is 0, since the x{\displaystyle x} value never increases or decreases. So, the slope of a vertical line will bey0{\displaystyle {\frac {y}{0}}}, and since you can't divide by 0, any number over 0 will always be undefined.


Problem: Write an article based on this summary: Anticipate the needs of the party. Add to party supplies or bring a gift for the host. Mention your potential contribution to the host. Accept the invite, or politely accept being turned down.

Answer: The kind of party being thrown will dictate the things that need to be available for the party to be a success! A dance party isn't much of a dance party without music, a wine tasting party could benefit from an intriguing vintage, and almost every large party needs ice at some point. By anticipating needs, you can prove to the host that you'd be a welcome addition to the party crew. There are cost effective ways of doing this, like making a dish to pass, or bringing suitable beverages. Think carefully about what you can bring to make the party even better, or bring a specific gift for the host that takes her tastes into consideration. For example, you might:  Bring seasonal gifts, like a plastic pumpkin of Halloween candy, eggnog, winter themed treats, or cold drinks in the summer. Give a mixology set as a present for when the party gets started, but only if age appropriate. A dish to pass or snacks to contribute. Now that you've figured out a worthwhile contribution, bring it up to the party host or organizers. For instance, if you have a delicious recipe for chocolate chip cookies, you can simply say something like:  "Emily, I heard about your party. Sound super fun! If you need any dessert, I make killer chocolate chip cookies - my grandmother's recipe. Everybody love them!" "So what are your plans for the weekend? Oh, a party? Well, if you need dessert, I have the best recipe for homemade chocolate chip cookies." If your offer matches the needs of the party or the tastes of the host, you'll almost certainly be invited! This scenario has the added benefit of not only getting you legitimately invited to the party, but you'll also be appreciated for your contribution to it! There's always a possibility, whether due to your associations or the hosts perceptions, that you might be denied. Getting angry in this situation rarely does anything positive for your reputation. Be polite and have fun on your own.


Problem: Write an article based on this summary: Mix the seed with sand. Spread the seed. Rake the area. Keep the seeds moist until the clover is established. Test your soil occasionally after your lawn is planted.

Answer:
Clover seeds are very small and lightweight. To ensure they spread evenly, it's best to mix them with another medium that will make them easier to distribute on the ground. You will need about 2 oz. (57 grams) of seed to cover 1000 square feet (93 sq. m.) of lawn. Before planting, mix your seeds with one of the following:  Soil (preferably unfertilized, to discourage the growth of weeds) Sand Sawdust Use your hand to spread the seed evenly over the lawn. If you have a large lawn, you can use a broadcast spreader, which you can buy at local garden stores and home improvement stores. You can also spread seed over large areas by smoothing the seed and sand mixture over the ground with a leaf rake turned so that the tines face up. Clover seeds will not grow if they are buried in the ground, but covering them with a thin layer of soil will help to keep them in place and prevent wind or predators from disturbing them. Go over the area you've seeded with a rake that is turned so that the tines face up, and gently mix the seeds into the top layer of soil. Do not rake more than a quarter-inch (6 mm) deep, otherwise the seeds won't grow. Water the seeds immediately after spreading them. This process will help the seeds stick in the ground and encourage germination. Provide the seeds with a light misting of water every day that it doesn't rain until the seedlings grow leaves.  During the spring, summer, and warmer fall months, make sure the clover gets about 1.5 to 2 inches (3.8 to 5 cm) of water per week. When planted during the warmer spring or summer months, clover seeds will germinate in one to two weeks. Make sure that the seeds do not have a chance to dry out during the day, or the sprouts will not survive. Once your clover lawn is established, take soil samples at least every 2-3 years. Check your soil nutrient and mineral levels, and make adjustments as needed. Try taking samples in spring one year, and in fall the next year. This will help give you an idea of which nutrients are most needed during different parts of the growing cycle.