Write the equation of the line in point-slope form that goes through the points (0, 1) and (2, 7)

Mathematics

1 answer:

laiz [17]2 years ago

4 0

Answer:

point - slope form

y - 1 = 3 (x-0)

Step-by-step explanation:

step(i):-

Given points are (0,1) and (2,7)

The slope of the line

$m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

$m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{7-1}{2-0} = \frac{6}{2} = 3$

m =3

Step(ii):-

point -slope form

y - y₁ = m(x-x₁)

Equation of the straight line passing through the point (0,1) and having slope 'm' = 3

y - 1 = 3 (x-0)

y -1 = 3x

3x - y +1=0

Equation of the straight line passing through the point (0,1) and having slope 'm' = 3 is 3x -y +1=0

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Solve for r 2r = 7/10

deff fn [24]

Answer:

7/20

Step-by-step explanation:

given,

2r = 7/10

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3 years ago

A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$