Blog 5: Multiple Representations Web for Linear Equations

I have not used the connection graph to situation but I am confident I can do so. Although, I will need to explore this connection.

Blog 6: y=mx + b

In the equation y=mx + b, m represents the slope and b represents the y- intercept. In a tile pattern, to determine the slope, you have to look for how much the right side of the tile pattern increases by when the left side is increased by one. To look for b, you have to see the number of tiles in figure zero. In a table, the slope is what y is when x is zero and b is also what y is when x equals zero. In an equation, m is the number being multiplied to x and b is the number being added or subtracted from it. Finally, in a graph, m is how steep the line is and b is where the line crosses the y axis. In a tile pattern, to determine the y-intercept, you have to see how many tiles are in figure zero. In a table, to determine the slope, you have to see hat y is when x is equal to zero. In an equation, to determine the y-intercept, you have to see what number is being added or subtracted. In a graph, you have to see where the line crosses the y-axis

Blog 7: Rates of Change and Slope

The rate of change is 10. The unit rate is 1/10, meaning for every hour studying, she earns a score of 10. If the line was steeper, she wouldn’t have to study as long to get a high score. If it was less steep, she would need to study more to get a high score. If the line sloped from the opposite direction, it would mean that slope turned negative. A line with a slope of zero would look horizontal, which would represent that she will receive the same score no matter how much time she spent studying. A line with an undefined slope looks vertical.

 Blog 8: Multiple Representations Web Continued

One connection I can do better at now is situation to graph, which was one connection I struggled with before.

Blog 9: Writing the Equation of a Line Through Two Points

To find the equation of a line using two points, the idea is substituting the variables in the equation y=mx+b. To do this, you first have to find the slope of the line. So, take any two points and subtract one x value from the other x value and one y value from the other y value. It doesn’t matter which way you choose, as long as you stick to it. Now, make that a fraction and simplify it. If you have to, flip it over to its vice versa to make it a whole number. This is your slope, or m. Now to find b, you have to substitute the x and y values in the equation y=(your slope)+b, with ones from a point. Once you’ve done so, just solve for b. Since you know what your slope is, it doesn’t matter which point you pick. Once you solved for b, rewrite the equation mx+b according to your numbers.

Example:
(8,16) (9,20) 20-16 = 4
9-8 =     1   =4

16=4(8)+b
16= 32+b
-32 -32
-16=b                                  Equation: y=4x-16