Graph of y = mx + c

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