Week 15 in Math 10

What we learned in week 15 in Math 10 is about a formula to get slopes and kinds of forms. The formula to get the value of a slope is pretty interesting for me. If the coordinates are (x1, y1) and (x2, y2), the formula is y1 – y2 over x1 – x2, so it means, we can the value of slope easily if we know ONLY the two coordinates on the line. A slope is the most important part of these units, and the forms are no exception. We learned two new forms in this week excepting Slope-Intercept Form which we already know. One of them is Pretty General Form, easily, the numbers must exist on only one side. It must consist of integers, it means there is NO fractions and decimals. Also, it must contain more positive numbers. For example, there is – x + y – 1 = 0, x – y + 1 is better. Another form is Point-Slope Form. The form is used when we know a coordinate and the slope. If we know the coordinate (x1, y2) and the slope is m, the formula of this form is y – y2 = m(x – x1).

For example,

1. When the two coordinates of the slope are (3, 7) and (5, – 13), the value of the slope.

  • The formula of a slope is y1 – y2 over x1 – x2.  We can substitute the coordinates on the formula, then, it is – 13 – 7 over 5 – 3. – 20 over 2 can be divided by 2, so it is – 10.
  • So, the slope is – 10.

2.

  • The slope is 4
  • The y-intercept is 2
  • The formula of the line is y = 4x + 2, so the formula of Pretty General Form is 4x – y + 2 =0.
  • We know a coordinate (1, 6) and the slope 4. The formula is y – y2 = m(x – x1). We should substitute the coordinate and slope. So, Point-Slope From is 4(x – 1) = y -6.

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