Write the equation of the line that passes through (3, 4) and (2, −1) in slope-intercept form.
a
y = 3x − 7
b
y = 3x − 5
c
y = 5x − 11
d
y = 5x − 9

Option C

y=5x-11

Step-by-step explanation:

We first find the gradient,m, of the line that passes through the points (3,4) and (2,-1)

Let

x=3

y=4

By substitution,

Putting that m=5, x=3 and y=4 into the general equation,

y=mx+c

This implies that

4=5(3)+c

4=15+c

4-15=c

c=-11

The equation of the line is given as

y=mx+c

where m=5 and c=-11

Hence y=5x-11

the ordered pairs for the given function are of the form

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough