Bell Work:

Factor:

mba – 7a + mbn – 7n

Answer:

(a + n)(mb – 7)

LESSON 106:LINEAR EQUATIONS, EQUATION OF A LINE THROUGH TWO POINTS

The graph of a first-degree equation in two unknowns is a straight line. this is the reason we call these equations linear equations.

The standard form of the equation of a straight line is

ax + by + c = 0

Where a, b, and c are constants (and where a and b are not both zero).

The following are equations of straight lines in standard form:

4x + y + 1 = 0

-2x – y – 11 = 0

We remember that if the equation of a line is written so that y is expressed as a function of x, such as

y = mx + b

We say that we have written the equation in slope-intercept form. In this equation m represents the slope of the line and b represents the y intercept of the line, which is the y coordinate of the point where the line in question crosses the y axis.

Thus far, we have learned how to draw the graph of a given linear equation and have learned how to find a good approximation of the equation of a given line. both of these exercises have helped us to understand the relationship between the equation of a line and the graph of a line.

We can determine the slope of a line by applying the slope formula that we learned in lesson 98.

m = y – y

x – x 2 1

2 1

Example:

Find the equation of the line that passes through the points (4, 2) and (-5, -3).

Answer:

Slope = 5/9

y = 5/9 x + b

(2) = 5/9(4) + b (-3) = 5/9(-5) + b

b = -2/9 b = -2/9

y = 5/9x – 2/9

Example:

Find the equation of the line that passes through the points (4, -2) and (-3, 4).

Answer:

Slope = -6/7

b = 10/7

y = -6/7x + 10/7

We see from these two examples that when we are given the coordinates of two points that lie on the line, the exact equation of the line can be determined. Estimated values of the slope and intercept are not acceptable for this type of problem.

Example:

Find the equation of the line that passes through the points (4, 3) and (4, -3).

Answer:

Equation of the line is x = 4.

Slope = undefined

HW: Lesson 106 #1-30