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1. State the points before you start working. For example: "My points are ( \( 1 \mathrm{p}, 1 \) ) and ( 4 , 10)." 2. Compute the slope, m , using the slope formula. If you compute a decimal, make sure to convertitto a fraction, so it is an exact answer. 3. Use the pointeslope form of a line to create the equation of the line going through the two points. If you have a special case of a line that is not a function, then just write the equation of the line and explain why you can't use the point-slope formula. 4. If possible, put the line in slope-intercept form and identify the y-intercept value as an ordered pair. Again, for those with special cases, give the equation of the line and the x-intercept. 5. Use Deamos or Craphmatica to graph your line. Adjust the axes so the \( y \)-intercept is shown and labeled. If your line does not have ay-intercept, still graph it, show and label the \( x \)-intercept, and explain why, in terms of grophing, it is not a function.

Ask by Mann Franklin. in the United States
Mar 16,2025

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**Points:** \( (1, 1) \) and \( (4, 10) \) **Slope (\( m \)):** 3 **Point-Slope Form:** \( y - 1 = 3(x - 1) \) **Slope-Intercept Form:** \( y = 3x - 2 \) with \( y \)-intercept at \( (0, -2) \) **Graph:** A straight line passing through \( (1, 1) \), \( (4, 10) \), and \( (0, -2) \). It is a function.

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Bonus Knowledge

When we talk about the slope of a line, we’re diving into the world of rise over run! The slope, \( m \), captures how steep a line is and the direction it goes: up and to the right for positive, down and to the right for negative. So, if you're working with points, remember to figure out the difference in their y-values (rise) and x-values (run) to find that slope. And if you hit a decimal during your calculations, turning it into a fraction keeps things neat and precise! Now, let's imagine applying this knowledge in real life: say you want to design a skateboard ramp! Knowing how to determine the slope will not only help you create a smooth ride but also ensure it's safe. You might use the slope to figure out how long your ramp needs to be based on the height you want it to reach. And remember, good design involves checking those calculations—one tiny mistake in the slope could mean a bumpy ride or worse, a wipeout! So, be thorough in measuring and calculating.

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