1. determine the equation of a line passing through the point (5, -3) with an undetermined slope.
2.use point-slope form to find the equation of the line passing through the point (0, 5) with a slope of 2/3.
3. use point-slope form to find a line passing through the point (2, 8) and parallel to the line = 5/6 x-1
4. use point-slope form to find a line perpendicular to y x = −2x+9 passing through the point (4, 7).
5. find the equation of a line passing through the points (-3, 6) and (1, 2).
6. find the equation of a line with an x-intercept (2, 0) and a y-intercept (0, 3)

Six questions in one post is a little beyond normal practice. Please limit your questions to three parts in the future.

1. Need a line through (5,-3) with undetermined slope m.

Using the poitn-slope form,

y-y1=m(x-x1) => y-5=m(x-(-3)) => y-5=m(x+3)

in standard form => y=m(x+3)+5.

2. Equation passing through (0,5) with slope m=2/3, in point-slope form.

Again, use point-slope form

y-y1=m(x-x1) => y-5=(2/3)(x-0) => y=2x/3+5

3. Equation through (2,8) parallel to line y1=5x/6-1

Using the poitn-slope form, with slope = 5/6 from parallel line

y-y1=m(x-x1) => y-8=(5/6)(x-2) => y=5x/6-5/3+8 => y=5x/6+19/3

4. Equation through (4,7) with slope perpendicular to line y=-2x+9

Slope required is perpendicular to line with slope -2.

The slope of the perpendicular is m=-1/(-2) =1/2

Using the poitn-slope form, with slope = 1/2 from perpendicular line

y-y1=m(x-x1) => y-7=(1/2)(x-4) => y=x/2-2+7 => y=x/2+5

5. Equation of line through (-3,6), (1,2)

It is easier to find slope of line then use point slope form than to use two-point formula.

Slope m = (y2-y1)/(x2-x1) = (2-6)/(1-(-3) = -4/4 = -1

Using the poitn-slope form, with slope = 1 from the given points,

y-y1=m(x-x1) => y-6=-(x-(-3)) => y=-x-3+6 => y=-x+3

6. Equation with x-intercept of (2,0) and y-intercept of (0,3)

Use the symmetric form: xi=2, yi=3 are intecept values

x/xi+y/yi=1 => x/2 + y/3 =1 => 3x+2y-6=0 if you wish.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!