A linear equation is a math sentence that shows that two expressions are equal. its general format is Y = mx + b

一次方程是一种数学表达式，用于表示两个式子相等。其一般形式为 y = mx + b。

--TASK--

"Now let's find out what 'linear' means, as well as the impact that changes in the 'size' and 'sign' (+ or -) of 'm' and 'b' have?" 

现在让我们来探究一下“线性”的含义，以及“m”和“b”的“大小”和“符号”（+或-）的变化会产生什么影响？

"To find out, go HERE and plot the following equations."

Y = X, Y = 2X, Y = 3X, Y = X + 1, Y = X - 1, and Y = -2X. 

Next, complete & copy the 3 paragraphs below:

1) "If we plot Y = X, Y = 2X, Y = 3X, Y = X + 1, Y = X + 2, Y = X - 1, and Y = -2X, we can see that they are all linear equations because ____."

2) "We can see that the bigger the value of 'm' (e.g., Y = 2X to Y = 3X), the steeper/flatter the line becomes; in addition, if the value of 'm' is positive (e.g., Y = 2X), then it always slopes upwards/downwards (from left to right), whereas if it's negative (e.g., Y = -2X), it slopes upwards/downwards"

3) "Furthermore, we can also see that the bigger the b-value (e.g., Y = X + 1, Y = X + 2), the more the line sh____. In addition, if the value of 'b' is positive (e.g., Y = X + 1), then it shifts leftwards/rightwards, whereas if it's negative (e.g., Y = X - 1), it shifts leftwards/rightwards."