point slope form?

Question

how would you write each equation in point slope form for the line that has a slope and cotains a point:

slope: 2/3, (5,6)

Answer 1

point slope form is: (y-y1)=m(x-x1),where m is slope

therefore, if you plug in the given slope and point, you get:

(y-6)=2/3(x-5)

y-6=2/3x-10/3
2/3x-y=8/3

you can't have a negative coefficient before x, so you move the y.

you also can't have fractions, so multiply by the lowest common denominator, which is 3

the result is: 2x-3y=8

by the way-y=mx+intercept ISN'T point slope formula--i just learned this in analytic geometry

Answer 2

Slope = the change of y over the change of x

6-3/ 5-2 = 3/3 = 1 The slope of those two points is 1

Answer 3

you're effectively given 2 factors in which your line passes, that's sufficient to define a rapidly line. One element you're given explicitly as (2, 4). The x coordinate of your different element is your x intercept. considering that's an x-intercept, the y coordinate of that element is straight away 0. Your 2d element is for this reason (-2, 0). From those 2 factors, you will discover a slope. Taking your unique element to be a million and your x intercept to be element 2, you get for the slope: m = (y2 - y1) / (x2 - x1) = (0 - 4) / ((-2) - 2) = (-4) / (-4) = a million This slope you are able to now plug into the element-slope form alongside with the two of your factors (i pick element a million) to get y - y1 = m * (x - x1) or y - 4 = a million * (x - 2) If we want, we can clean up for y and alter this into slope-intercept form, giving y = x + 2

Answer 4

point slope form is

y = m*x +intercept

thus

m= slope = 2/3

and you know x=5 when y = 6 so

6= 2/3 * x + 5

therefore, 0= 2/3 *x -1

y= 2/3 * x -1 :)

Answer 5

equation of line in point slope form

y - y1 = m(x - x1) where m =slope and point (x1,y1)

y - 6 = 2/3(x - 5)

3(y-6) = 2(x-5)

3y - 18 = 2x - 10

3y - 2x -18+10 = 0

3y - 2x - 8 = 0

Answer 6

If you're trying to figure out the equation of the line you would plug in the points in y=mx+b
m=2/3 and you would have to solve for b

1. plug it in
6=2/3(5)+b

2. solve
6=10/3+b

3. subtract 10/3 on each side
8/3=b

your equation will be y=2/3x+8/3

Answer 7

y - y1 = m (x - x1)

y - 6 = 2/3 (x - 5)

y = (2/3)x + 6 - 10/3

y = (2/3)x + 8/3

Answer 8

use the formula to find the intercept
y=mx+b
6=2/3*5+b
1.67 = b
y=.67x + 1.67