In this chapter, we will learn graph of linear equation y = mx + c and understand various parameters like slope, x intercept and y intercept.

## Drawing graph of y = mx + c

Understand that the expression y = mx + c is a linear equation, so the **graph will be a straight line**.

To draw its graph, we need at least two points.

**For first point, put x = 0.**

y = m(0) + c

y = c

So, (0, c) is the first point.

**For second point, put y = 0**

y = mx + c

0 = mx + c

x = -c / m

So, ( -c/m, 0) is the second point of the equation.

Plotting both the points on graph and join them with the straight line.

The above blue line represents the linear expression y = mx + c

Now let us understand different characteristics of above expression.

### Slope of line y = mx + c

Slope of equation **tells the steepness and direction of straight line**. The more the slope, the more tilted the line will be with respect to x axis.

Slope of any line is given by **tanθ**.

Consider triangle OAB in the above graph.

\mathtt{tan\theta \ =\ \frac{Perpendicular}{Base}}\\\ \\ \mathtt{tan\theta =\frac{OA}{OB}}\\\ \\ \mathtt{tan\theta =\frac{c}{c/m}}\\\ \\ \mathtt{tan\theta =m}

Hence, the slope of the above equation is ” m “.

### x intercept of line y = mx + c

The distance of the origin from the point of intersection of x axis & given line is called x intercept.

We know that line y = mx + c cuts the x axis at point B. So the distance OB is the x intercept line.

In the above figure distance of OB is given as, OB = -c/m

Hence, **-c/m is the value of x intercept**.

### y intercept of line y = mx + c

The distance from origin to the intersection of line and y axis is called y intercept.

In the given figure, the line y = mx + c intersect at point A. So the distance OA is the y intercept.

The distance OA is given as; OA = c

Hence, **“c” is the value of y intercept**.

I hope you understood the above concept. Let solve some problems for further understanding.

### Problems on equation y = mx + c

(**01) Find the x and y intercept of equation 2x + 4y = 3****Solution**

First convert the given equation in form of y = mx + c

Putting the values;

\mathtt{2x+4y\ =\ 3}\\\ \\ \mathtt{4y\ =\ -2x+3}\\\ \\ \mathtt{y\ =\ -\frac{2x}{4} +\frac{3}{4}}\\\ \\ \mathtt{y\ =\ -\frac{x}{2} +\frac{3}{4}}

Here, m = -1/2 and c = 3/4.**X intercept = -c/m**

Putting the values;

\mathtt{\Longrightarrow \ \frac{-3}{4} \div \frac{-1}{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-3}{4} \times \frac{-2}{1}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{2}} \\ \\

Hence,** value of x intercept is 3/8.**

**y intercept = c**

Putting the values;**y intercept = 3/4**

**Example 02**

Find the angle formed by line 2y = 2x + 6 from x axis.

**Solution**

First represent the equation in form of y = mx + c

\mathtt{2y\ =\ 2x\ +\ 6}\\\ \\ \mathtt{y\ =\ \frac{2x}{2} +\frac{6}{2}}\\\ \\ \mathtt{y\ =\ x\ +\ 3}

On comparing, we get m = 1 and c = 3.

We know that slope of line is given by m.

\mathtt{tan\theta \ =\ m}\\\ \\ \mathtt{tan\theta \ =\ 1}\\\ \\ \mathtt{\theta \ =\ 45\ degree}

Hence, **the line make 45 degree from x axis.**

**Example 03**

Find slope, x intercept and y intercept of following equation.

y + 3x + 8 = 0

**Solution**

First represent equation in form of y = mx + c

y = – 3x – 8

Here m = -3 and c = -8.**Slope of equation **= m = -3

Value of x intercept = -c/m

Putting values we get;**Value of x intercept** = – (-8)/(-3) = -8/3

**Value of y intercept **= c = -8