1. write an equation for a line that has a slope of 2/3 and a y intercept of 7

2 write an equation for a line that passes through the points (2,3) and (3,5).

1. Y=2/3x+7

2. Y=2x-1

Step-by-step explanation:

It a begins with y=mx+b, the equation of line,

m= slope

b= y-intercept (or in other words the value of y when x=0)

(y just stands for the value of y)

for example, let's use the equation for #1, y=2/3x+7. let's say our input, or x-value is 3, so it'll be

y=2/3(3)+7

y=2+7

y=9

so in coordinate form it would be (3,9)

in order to figure out how to find the equation of line for a problem like #2 it's a little different;

m= y2-y1/x2-x1

m= 5-3/3-1

m=2/1

m=2

so in order to do this you'll have to take the coordinate with the larger x-value and plug it into x2, and the y-value for x2 becomes y2, and the lower x-value becomes x1 and the y-value becomes y1. it may be hard to see on this but this is what it should look like on a piece of paper;

y2-y1

m= x2-x1

so just substract and simplify, it doesn't have to be a whole number, it can be a fraction as well.

now onto b;

you multiply the x-value giving to you (it has to be one of the coordinates given to you) by m,

2(2)=4

4+b=3 (the 3 is the y-value in the coordinate you chose)

-4 -4 (then substract 4 from both sides to isolate b)

b= -1

(if the number you got when you multiplied the x-value by m is equal to the y-value in that coordinate then there isnt a b so it'd be y=mx+0 but if you're doing this for a class your teacher might want you to include that +0 part)

so yeah that's it have a good day and good luck :D

understand that i don't know the answers

will someone answer his question

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c