Intercepts on the axes
We say that the line y = mx + c intersects the y  axis, at the point (0,C) Justification: any point on the y  axis has x  coordinate = 0. Since the line crosses y  axis, the point of intersection of the line y = mx + c and y  axis has x  coordinate = 0 putting x = 0 in y = mx + c we get y = c.
Now we can say that the line y = mx + c makes an intercept c on the yaixs. Hence for finding an intercept made on the y  axis by any line, we must put x = 0 in the equation and find y.
Similarly for finding x  intercept of a line put y = 0 in the equation of the line and find x.
Example Find the intercept made by the line 2y  3x = 7 on both the coordinate axes.
Solution :
Putting x = 0 in 2y  3x = 7 we get 2y = 7
\ y = 7/2
which means the line makes an intercept 7/2 on the yaxis
Putting y = 0 in 2y  3x = 7 we get 3x = 7
\ x = 7/3
Which mean the line makes an intercept 7/3 on the x  axis.
Slope and intercept from (equation) of line
Any straight line expressed in this form always takes the form y = mx + c where m stands for the slope and c stands for the y  intercept of the line which involves two relationships.
 The slope
 The intercept i.e. the point at which the line crosses the y  axis. When an equation is put in the form y = mx + c it is said to be in y  form or slope  intercept form.
Example State the slope and y  intercept of the straight line y = x + 7
Solution : y = x + 7 comparing it with y  form as
y = mx + c i.e.
slope m = 1 and y  intercept (c) = 7
Example Show that the lines given by 3x + 4y 3 = 0 and 6x + 8y 7 = 0 are parallel.
Solution : Ist line is 3x + 4y  3 = 0
Putting in y  form, we get,
Therefore slope m_{1} = 3/4
Also, the second line is 6x + 8y 7 = 0
putting in y  form, we get,
Therefore, slope m_{2} = 3/4
Since m_{1} = m_{2}, the two lines are parallel
Thus when an equation is put in the form y = mx + c
i.e. y  form, it should be evident that the slope is the same as the coefficient of x term.
