**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

**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

Add 6 to both sides.

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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