I learned forms of equations this week. These forms are:
- Slope intercept form
- Point slope form
- General form
Slope intercept form: This form can be used when we know the slope of line and the y-intercept of the line. The form looks like that:
y = mx+b. Here m is the symbol of slope and b is the symbol of y-intercept.
Example: Determined the equation of the line with slope 3 and y-intercept 4
Answer: y = 3x+4
As we can see, 3 came before x and 4 came before y-intercept.
Point slope form: This form can be used when we know the slope of a line and the coordinates of any point of that line and when we don’t know the y intercept. The form looks like this: m(x-x1) = y-y1. This is a form in which the subtraction of the y value from the first y value is equal to the product of the slope of the subtraction of the first x value from the x value. Here x1 and y1 represent the (x1,y1) coordinates.
Example: State the equation of the line with the slope 5 and point (6,8)
Answer: 5(x-6) = y-8
As we can see, the multiplication of x from 6, that is, from the point corresponding to the x-axis of any coordinate on the line, multiplied by 5, that is, multiplied by the slope, is the subtraction of y from 8, that is, from the point corresponding to the y-axis of any coordinate on the line. It is an equality whose inference is equal to.
General Form: In this form, the right side of the equation is equal to 0 and all other terms are written on the left side of the equation. In this form, there are no fractions, only integers, and the leading coefficient cannot take a negative value. The form looks like this: Ax+Bx+C = 0. In this form A B and C expressed as integers. Although this is not a very useful form, it is a form that makes it easier to write code blocks and looks neat in appearance.
Example: Find the equation in general form with slope 7 and point (2,9)
Answer: In order to write in general form, it would be easiest to first find the point slope form with these given values and then convert this form to general form.
As we can see, after writing it as a point slope form, I distributed 7 into the parentheses and then, depending on whether the coefficient of x is negative or not, I threw the things on the right side of the equation to the other side, thus making the right side of the equation zero.