Find the equation of the line with y-intercept -2 and passing though the point (2,5). show your work. what is the equation of a line perpendicular to this line, but with the same y-intercept? (have no idea how to do this can someone explain)

equation of a line with y intercept of neg.2 is y=mx-2

you could use pint slope[y-y1=m(x-x1)], but i preffer slope intercept form [y=mx+b]

5=m2-2

move 2 to the other side

7=m2

divide both sides by 2

3.5=m

so, the slope is 3.5

equation for a line that passes through point (2,5) with a y intercept of -2 is y=3.5x-2

the equation of a perpendicular line to the line y=3.5x-2 has a slope that is negative reciprical of 3.5

we keep the everything on y=3.5x-2 same except the slope.

negative reciprical slope of 3.5 is -

simplify

so, the equation of a line perpendicular to the first one is y=-2/7x-2

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: