Question

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 please explain)

Answer 1

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 -

$- \frac{10}{35}$

simplify

$- \frac{2}{7}$

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