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: howdy

step-by-step explanation: