16JUL21

A line makes x-intercept 2 and y-intercept 3. What is its equation?


A line passes through (2,5) and (4,9). What is its equation?


A line passes through (1,1) and (2,2). What is its equation?


Four ways of writing the equation:

1. Slope-intercept form

2. Point form

3. Intercept form

4. Observing the pattern of coordinates


(1,1), (2,2)

y=x


(1,-1), (2,-2)

y=-x


(1,2), (2,3), (3,4)

y=x+1


(1,0), (2,1), (3,2)

y=x-1


(1,3), (2, 5), (4,9)

y=2x+1


(2,3), (3,5), (4,7)

y=2x-1


(2,4), (3,6), (4,8)

y=2x


(3,1), (6,2), (9,3)

y=x/3 or 3y = x


If slope is positive, it's a line leaning against the right wall. If slope is negative, it's a line leaning against the left wall.

A constant term in the equation indicates the line cuts the y-axis somewhere. If there is no constant in the equation, it means the line passes through the origin.

If the slope of two line is the same, they are parallel.

If the product of the slopes of two lines equals -1, they are perpendicular.


(1)y=2x

(2)y=2x+3

(1) passes through origin. (2) doesn't.

They are parallel.

y=(-1/2)x+... will be perpendicular to the above lines.


(2,4), (3,9), (4,16), (5,25)

y=x^2

This is not a LINEAR equation.

In a linear equation, the power of x and y should be 1.

Since this is not a linear equation, it doesn't make a straight line. It's a curve, called a parabola.


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