Question

of lines with the following characterizing property. (h) mar + 2) = -1 (b) perpendicular to 3r + 2y = 7 (d) having inclination 60° (f) passing through the origin (h) having slope 6) x-intercept twice y-intercept

Answer 1

We need to write the equation of the family of the lines with the following characterizing property.

j) x - intercept is twice y - intercept

X- intercept is the value of x when y= 0

Y- intercept is the value of y when x = 0

so, let y- intercept = a

x- intercept = twice y- intercept = 2a

So, the line will pass through the points: ( 2a , 0 ) and ( 0 , a )

The general equation of the line is : y = m * x + b

Where m is the slope and b is y - intercept

$slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{a-0}{0-2a}=\frac{a}{-2a}=-\frac{1}{2}$

So, the equation of the family will be :

$y=-\frac{1}{2}x+a$