**Finding the slope and y-intercept of a linear function worksheet :**

Here we are going to see some practice questions on finding slope and y-intercept of a linear function.

**Y-intercept :**

The y-intercept of the line is the value of y at the point where the line crosses the y axis.

**How to find slope :**

To find the slope from a graph first we have to mark any two points on the graph.

After marking two points we have to draw the right triangle which connects the points which have been marked. In the right triangle,

- the vertical direction at the line is called "rise"
- the horizontal direction at the line is called "run"

**Alternate method :**

We can use the formula (y₂-y₁)/(x₂-x₁) to find the slope of the line. Here (x₁, y₁) and (x₂, y₂) are any points lie on the line.

**Problem 1 :**

Find the slope and y-intercept of a linear function from the graph given below.

**Problem 2 :**

Find the slope and y-intercept of a linear function from the graph given below.

**Problem 3 :**

Find the slope and y-intercept of a linear function from the graph given below.

**Problem 1 :**

Find the slope and y-intercept of a linear function from the graph given below.

**Solution :**

**Y-intercept :**

The y-intercept of the line is the value of y at the point where the line crosses the y axis.

The above line intersects the y-axis at the point 4. So y-intercept = 4 Finding the slope and y-intercept of a linear function worksheet

**Slope :**

Now we are going to mark two points (-2, 0) and (0, 4) on the line to find the slope.

Slope = Change of y/change of x

**"We have to rise before we run"**

We need to take downward direction from (0,4) for rise.Since we take downward direction we have to put negative sign.

Rise = -4

After reaching the common point we need to move towards to the left ward 2 units. So we have to take -2.

Run = -2

= (- 4) / (-2) = 2

Hence, slope of the given line is 2.

By using the alternative method, we will get the same answer.

m = (y₂-y₁)/(x₂-x₁)

(x₁,y₁) ==> (-2, 0) and (x₂, y₂) ==> (0, 4)

m = (4 - 0)/(0 + 2)

m = 4 /2 = 2

**Problem 2 :**

Find the slope and y-intercept of a linear function from the graph given below.

**Solution :**

**Y-intercept :**

The y-intercept of the line is the value of y at the point where the line crosses the y axis.

The above line intersects the y-axis at the point -3. So y-intercept = -3

**Slope :**

Now we are going to mark two points (1, -1) and (2, 1) on the line to find the slope.

Slope = Change of y/change of x

**"We have to rise before we run"**

We need to take downward direction from (2,1) for rise.Since we take downward direction we have to put negative sign.

Rise = -2

After reaching the common point we need to move towards to the left ward 1 unit. So we have to take -1.

Run = -1

= (-2) / (-1) = 2

Hence, slope of the given line is 2.

By using the alternative method, we will get the same answer.

m = (y₂-y₁)/(x₂-x₁)

(x₁,y₁) ==> (1, -1) and (x₂, y₂) ==> (2, 1)

m = (1 + 1)/(2 - 1)

m = 2 / 1 = 2

**Problem 3 :**

Find the slope and y-intercept of a linear function from the graph given below.

**Solution :**

**Y-intercept :**

The y-intercept of the line is the value of y at the point where the line crosses the y axis.

The above line intersects the y-axis at the point 3. So y-intercept = 3

**Slope :**

Now we are going to mark two points (0, 3) and (-5, 1) on the line to find the slope.

Slope = Change of y/change of x

**"We have to rise before we run"**

We need to take downward direction from (0,3) for rise.Since we take downward direction we have to put negative sign.

Rise = -2

After that we need to move towards to the left ward 5 unit. So we have to take -5.

Run = -5

= (-2) / (-5) = 2/5

Hence, slope of the given line is 2/5.

By using the alternative method, we will get the same answer.

m = (y₂-y₁)/(x₂-x₁)

(x₁,y₁) ==> (-5, 1) and (x₂, y₂) ==> (0, 3)

m = (3 - 1)/(0 - (-5))

m = 2 /(0 + 5) = 2/5

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