Question

23. Which line has the equation y = -x + 3?

a. Line DF
b. Line DE
c. Line GE
d. Line GF
24. Which line has the equation x - 3y = 3?

a. Line DF
b. Line DE
c. Line GE
d. Line GF

Answer 1

the line equation passing through two points is find by
\[\Large y-y_{0}=m(x-x_{0})\]
first of all slope is calculated.
for example if a line pass through (5,3) and (7,9) then slope will be
\[\Large m=\frac{9-3}{7-5}=3\]
now you can use any points in these two, to get line equation in this case using first point (5,3)
\[\Large y-3=3(x-5)\]
simplify
\[\Large \implies y=3x-12\]

in your case you are given two points for each line through which they pass .
just find the slope of the lines . then use any point to get equation of line .

Answer 2

@JeremiahJallo can you do this now ??

Answer 3

There are two questions here. Looking at the first one only, you will notice that it is already in slope intercept form. Therefore, it is very simple to get the slope value as it is the coefficient of the x term which is a -1. A negative slope means the line runs "down hill." Looking at your figure, there are only two lines that fall in that category. Line DE and line FG, Your chances are now 50/50. But Hark, no need to guess the equation provided you with the x intercept, when x=0, y will then =3. Isn't math fun?

Answer 4

Suggest you convert the 2nd equation to the same form as the first or "slope intercept" and analyze it in a similar fashion. Try it, you'll like it.