find a slope
2
-1/2
-2
1/2
Well, you're really giving me a range of slopes here! It's like playing a game of "Slope Roulette". So, let's see what we've got:
- "2" is a pretty steep slope. It's like a mountain-climbing adventure. Hold on tight!
- "-1/2" is a gentler slope, like a pleasant stroll downhill. Just enjoy the breeze, but watch your step!
- "-2" is even steeper than "2"! It's like skiing down a black diamond slope. Make sure you're prepared for the adrenaline rush!
- "1/2" is a milder slope, more like a gentle slide at a playground. Enjoy the leisurely descent!
Remember, these slopes represent the change in y divided by the change in x. So, next time you're out and about, keep an eye out for slopes and let the good times roll!
To find the slope of a line, you need two points on that line. The slope is defined as the change in y-coordinates divided by the change in x-coordinates. Let's use the two points (2, -1/2) and (-2, 1/2) to find the slope.
Step 1: Identify the coordinates of the first point as (x₁, y₁) = (2, -1/2), and the coordinates of the second point as (x₂, y₂) = (-2, 1/2).
Step 2: Calculate the change in y-coordinates (Δy) by subtracting the y-coordinate of the first point from the y-coordinate of the second point: Δy = y₂ - y₁ = (1/2) - (-1/2) = 1/2 + 1/2 = 1.
Step 3: Calculate the change in x-coordinates (Δx) by subtracting the x-coordinate of the first point from the x-coordinate of the second point: Δx = x₂ - x₁ = -2 - 2 = -4.
Step 4: The slope (m) is the ratio of Δy to Δx: m = Δy / Δx = 1 / -4.
Therefore, the slope of the line passing through the points (2, -1/2) and (-2, 1/2) is -1/4.