We have seen here when graphing linear relationships that the equation for a straight line can be given in the form y = mx + b. This form is known as the Slope Intercept Form and it is a most useful form as it immediately shows two important things about any straight line when graphed on a Cartesian plane; the slope m, and the yintercept b.
There are other forms of the equation of a straight line and the examples below will show how to convert from these to the slope intercept form.
There is more here on the slope of a line so we will start by looking at the yintercept.
The yintercept is the point at which a straight line intersects the yaxis. At this intersection point the value of x is always 0 so the yvalue can be found algebraically simply by substituting 0 for x in the equation that represents the line as the example below shows.
Try the graph generator with different values for the yintercept (and the slope too if you wish) to see the effect on the line.
As shown earlier, finding the yintercept is straightforward if the equation of the line is given in slope intercept form. e.g. for a line with equation y = 3x  7, the yintercept is at point (0, 7). If the equation is given in a different form then it can require additional steps as the two examples below show:
Find the yintercept for line with equation 3x + 4y = 12 

substitute 0 for x  (3 x 0) + 4y = 12 4y = 12 
Divide both sides by 4 to isolate y  4y ÷ 4 = 12 ÷ 4 y = 3 
yintercept is at point (0,3) 
Find the yintercept for line with equation 5x + 7y = 14 

substitute 0 for x  (5 x 0) + 7y = 14 7y = 14 
Divide both sides by 7 to isolate y  7y ÷ 7= 14 ÷ 7 y = 2 
yintercept is at point (0,2) 
The equation of a straight line can be given in different forms. The form y = mx + b is the most common and is known as the Slope Intercept Form. It is not the only form though; for example the equation ax + by = c is shown in what is known as standard form.
Two benefits of the slope intercept form is that both the slope (m) and the yintercept (b ) are immediately obvious. Let us convert the example above from standard form to slope intercept form:
Convert 3x + 4y = 12 

subtract 3x from both sides  3x  3x + 4y = 3x + 12 4y = 3x + 12 
Divide both sides by 4 to isolate y  4y ÷ 4= (3x ÷ 4) + (12 ÷ 4) y = (3/4)x + 3 y = 0.75x + 3 
Convert 5x + 2y = 15 

add 5x to both sides  5x  5x + 2y = 5x + 15 2y = 5x + 15 
Divide both sides by 2 to isolate y  2y ÷ 2= (5x ÷ 2) + (15 ÷ 2) y = (5/2)x + 7.5 y = 2.5x + 7.5 
What is the equation of a line that passes through point (5,6) and has a slope of 3? 

Substitute (5,6) for x and y and 3 (slope) for m in the equation in slope intercept form (y = mx + b)  6 = (3x5) + b 6  15 = b b = 9 
Use the values of m and b to write the equation  y = 3x  9 
Use the worksheet(s) below for practice.