Question

Find the horizontal and vertical intercepts, estimate to the nearest tenth?

Answer 1

Visual `ul("estimates")`

`y_("intercept") = 2.5 = 2 5/10`
`x_("intercept")=1.6 =1 6/10`

Explanation:

`1.5< x_("intercept") < 2 color(white)("ddd")->color(white)("ddd")` I choose `1.6 =1 6/10`

`y_("intercept") = 2.5 = 2 5/10`

Note that the question stipulates that we must use tengths

Answer 2

Calculating the intercepts and rounding to the closest tenth gives `(0,2.5),(1.7,0)`

Explanation:

I'm going to approach this question by not visually estimating but instead calculating and then rounding, if needed, to the nearest tenth.

There are two points that we can use with a high level of certainty: `(-1,4),(1,1)`

We can find the slope that results from connecting these two points:

`m=(y_2-y_1)/(x_2-x_1)=(1-4)/(1-(-1))=(-3)/(2)=-3/2`

And then we can use the point slope formula to find the equation of the line:

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

`(y-4)=-3/2(x-(-1))`

`(y-4)=-3/2(x+1)`

I'll change this into the slope intercept form to better look at the intercepts:

`y=-3/2x-3/2+4`

`y=-3/2x+5/2`

When `x=0, y=5/2=2.5`

When `y=0`, we get:

`0=-3/2x+5/2`

`3/2x=5/2`

`3x=5=>x=5/3~~1.7`