Question

x-intercept=2; containing the point (-5,4), using either the general form or the slope-intercept form of the equation of a line.

Answer 1

x intercept 2 means you know that
\[(2,0)\] is on the graph

Answer 2

so you have two points,
\[(2,0),(-5,4)\] find the slope via
\[m=\frac{y_2-y_1}{x_2-x_1}\] and then use the point slope formula
\[y-y_1=m(x-x_1)\]

Answer 3

clear or you need it worked out?

Answer 4

wait? my bad its (4,-5)

Answer 5

ok fine, then the two points are
\[(2,0)\] and
\[4,-5)\] but the formulas are still the same

Answer 6

\[m=\frac{0-(-5)}{2-4}=\frac{5}{-2}=-\frac{5}{2}\]

Answer 7

is the answer y=-5/2-5?

Answer 8

close

Answer 9

+5?

Answer 10

it is
\[y=-\frac{5}{2}x+5\]

Answer 11

hold on

Answer 12

\[y-0=-\frac{5}{2}(x-2)\]
\[y=-\frac{5}{2}x+5\]
right, that is correct

Answer 13

can you help me with this problem?

Answer 14

The endpoints of the diameter of a circle are (-3,2) and (5,-6). Find the center and radius of the circle. Write the general equation of this circle.

Answer 15

name it

Answer 16

sure no problem

Answer 17

you know it should look like
\[(x-h)^2+(y-k)^2=r^2\] where the center is (h,k) and the radius is r

Answer 18

so what we need is the center and the square of the radius. the center is the midpoint of the line, which you find by adding each coordinate and dividing by 2 (take the average)

Answer 19

endpoints are
(-3,2) and (5,-6). so the center is
\[(\frac{-3+5}{2},\frac{2-6}{2})\]or
\[(1,-2)\]

Answer 20

(1,-2)

Answer 21

exactly

Answer 22

so now we know it looks like
\[(x-1)^2+(y+2)^2=r^2\] and we only need
\[r^2\]

Answer 23

the square of the distance between (1,-2) and (-3,2) is
\[(1+3)^2+(2+2)^2=4^2+4^2=16+16=32\]

Answer 24

so your "final answer" is
\[(x-1)^2+(y+2)^2=32\]

Answer 25

you did the distance formula right?