# DETERMINING SLOPE AND Y INTERCEPT

## About "Determining slope and y intercept"

Determining slope and y intercept :

The graph of every non vertical line crosses the y-axis. The y-intercept is the y-coordinate of the point where the graph intersects the y-axis. The x-coordinate of this point is always 0.

When the equation of a line is given in the form

y = mx + b (slope-intercept form)

we can easily determine the slope and y-intercept. That is, the coefficient of x is slope and the number added to x-term is y-intercept.

More clearly,

Slope  =  m

Y-intercept  =  b

## Determining slope and y intercept - Examples

Example 1 :

Determine the slope and y-intercept of the line whose equation is y = -3x + 4.

Solution :

When the given equation y = -3x + 4 is compared to the form

y = mx + b,

we get

slope m  =  -3

y-intercept  b  =  4

Example 2 :

Determine the slope and y-intercept of the line whose equation is y = 5x.

Solution :

When the given equation y = 5x is compared to the form

y = mx + b,

we get

slope m  =  -3

y-intercept  b  =  0

Example 3 :

Determine the slope and y-intercept of the line whose equation is 2x + y - 6  =  0.

Solution :

The given equation 2x + y -6 = 0 is not in the form

y = mx + b

Step 1 :

Write the given equation in the form y = mx + b.

2x + y - 6  =  0

Subtract 2x from both sides.

y - 6  =  -2x

y  =  -2x + 6

Step 2 :

Compare the equation y = -2x + 6 with y = mx + b.

Slope m  =  -2

Y-intercept b  =  6

Example 4 :

Determine the slope and y-intercept of the line whose equation is x + 3y  =  5.

Solution :

The given equation x + 3y  =  5 is not in the form

y = mx + b

Step 1 :

Write the given equation in the form y = mx + b.

x + 3y  =  5

Subtract x from both sides.

3y  =  -x

Divide both sides by 3.

y  =  -x/3

Step 2 :

Compare the equation y = -x/3 with y = mx + b.

Slope m  =  -1/3

Y-intercept b  =  0

After having gone through the stuff given above, we hope that the students would have understood, how to determine the slope and y-intercept when the equation of a straight line is given in the form y = mx + b.

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