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

Question

Julia Adams · Accepted Answer

Visual #ul("estimates")#

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

Genesis Allen · Answer

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

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#

Hazel Anglin · Answer

undefined To find the horizontal intercept (x-intercept) of a function, set $ y $ (or $ f(x) $) to zero and solve for $ x $. To find the vertical intercept (y-intercept), set $ x $ to zero and solve for $ y $.