**Deriving the slope intercept form of an equation :**

**In this section, we are going to see, how to derive the slope intercept form of an equation. **

**Step 1 :**

Let L be a line with slope m and y-intercept b. Circle the point that must be on the line. Justify your choice.

(b, 0) (0, b) (0, m) (m, 0)

The coordinate of x is 0 in the point that includes the y-intercept.

**Step 2 :**

Recall that slope is the ratio of change in y to change in x. Complete the equation for the slope m of the line using the y-intercept (0, b), and another point (x, y) on the line.

Slope m = change in y-values / change in x-values

Slope m = (y - b) / (x - 0)

Slope m = (y - b) / x

**Step 3 :**

In an equation of a line, we often want y by itself on one side of the equation. Solve the equation from Step 2 for y.

m = (y - b) / x

Multiply both sides by x

m.x = [(y - b) / x].x

mx = y - b

Add b to both sides of the equation.

mx + b = (y - b) + b

mx + b = y

Write the equation with y on the left side.

y = mx + b

Critical thinking : Write the equation of a line with slope m that passes through the origin. Explain your reasoning.

y = mx

Because the origin is on the y-axis, the graph crosses the y-axis at (0, 0). So, the y-intercept b is 0, and y = mx + b becomes y = mx.

**Example 1 : **

A line is passing through the points (2, 3) and (0, 4). Find the equation of the line in slope intercept form.

**Solution :**

**Step 1 : **

Fine the slope of the line using the points (2, 3) and (0, 4).

Slope m = change in y-values / change in x-values

Slope m = (4-3) / (0-3)

Slope m = 1 / (-3)

Slope m = -1/3

**Step 2 : **

In the point (0, 4), x-coordinate is zero. So, the line intersects y-axis at this point.

Since the y-coordinate at this point is 4, y-intercept is 4.

Hence, the equation of the line is y = (-1/3)x + 4.

**Example 2 : **

A line is passing through the points (0, 0) and (-1, -8). Find the equation of the line in slope intercept form.

**Solution :**

**Step 1 : **

Fine the slope of the line using the points (0, 0) and (-1, -8).

Slope m = change in y-values / change in x-values

Slope m = (-8-0) / (-1-0)

Slope m = -8 / (-1)

Slope m = 8

**Step 2 : **

Since the line is passing through the origin (0,0), there is no y-intercept or y-intercept = 0.

Hence, the equation of the line is y = 8x.

After having gone through the stuff given above, we hope that the students would have understood, how to derive the slope intercept form of an equation.

Apart from the stuff given above, if you want to know more about "Deriving the slope intercept form of an equation", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**