Question

Determine the intercepts of the line that passes through the following points. (-15,5) (-9,10) (-3,15)

Answer 1

We check the collinearity of points. If the points A(-15, 5), B(-9, 10) and C(-3, 15) are collinear, then the lines AB and BC are the same slope.

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

Substitute:

`AB:\ m=(10-5)/(-9-(-15))=(5)/(-9+15)=(5)/(6)\\\\BC:\ m=(15-10)/(-3-(-9))=(5)/(-3+9)=(5)/(6)`

A, B and C are collinear.

The slope-point form:

`y-y_1=m(x-x_1)`

Substitute:

`y-5=(5)/(6)(x-(-15))\\\\y-5=(5)/(6)(x+15)\qquad|\text{use distributive property}\\\\y-5=(5)/(6)x+(75)/(6)\qquad|+5=(10)/(2)\\\\y=(5)/(6)x+(25)/(2)+(10)/(2)\\\\y=(5)/(6)x+(35)/(2)`

x-intercept: put y = 0 to the equation

`0=(5)/(6)x+(35)/(2)\qquad|-(35)/(2)\\\\(5)/(6)x=-(35)/(2)\qquad|\cdot6\\\\5x=-3\cdot35\qquad|:5\\\\x=-3\cdot7\\\\x=-21`

y-intercept: put x = 0 to the equation

`y=(5)/(6)(0)+(35)/(2)\\\\y=(35)/(2)\to y=17.5`