Question

The points (–4, –3) and (–1, –8) are on a line. Find the intercepts to the nearest tenth.

A) x = –5; y = –11
B) x = –5.8; y = –9.7
C) x = 3; y = –5
D) x = 5.8; y = –9.7

Answer 1

B) intercepts are
`x=-5.8\ and\ y =-9.7`

Explanation:

Given coordinates are
`(-4,-3)\ and\ (-1,-8)`

The intercepts are the points where the line meets with the x-axis and the y-axis.

The Y-intercept is where x-coordinate is zero.

And X-intercept is where y-coordinate is zero.

We will use the slope intercept form of equation of line to compute Y-intercept.

`y=mx+b`

Where
`m` is slope of line. And
`b` is Y-intercept.

We will find slope of line and plug in this equation to compute Y-intercept.

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

`x_1=-4,y_1=-3\ and\ x_2=-1,y_2=-8\\\\m=(-8-(-3))/(-1-(-4))\\m=(-5)/(3)`

`Plug\ x=-4,y=-3\ in\ y=mx+b\\\\-3=(-5)/(3)*-4+b\\\\-3=(20)/(3)+b\\\\-3=6.67+b\\-3-6.67=b\\\\b=-9.7`

`y=(-5)/(3)x-9.7`

Now, plug
`y=0` in the equation
`y=mx+b` to find X-intercept.

`0=(-5)/(3)x-9.7\\ \\9.7=(-5)/(3)x\\\\9.7*3=-5x\\\\x=-9.7(3)/(5)\\ \\x=-5.8`

So, our intercepts are
`x=-5.8\ and\ y =-9.7`