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3 years ago

Line CD passes through (0, 1) and is parallel to x + y = 3. Write the standard form of the equation of line CD.

Mathematics

2 answers:

ioda3 years ago

7 0

A. would be the correct choice because the x+y hast to =1.

mylen [45]3 years ago

7 0

Answer: a. $x+y=1$

Step-by-step explanation:

Given: Line CD passes through (0, 1) and is parallel to $x+y=3$ .

We know that if two line are parallel then they have equal slopes.

Thus, the slope of line = slope of line $x+y=3$ .

$x+y=3\\\Rightarrowy=3-x$ when we compare this to the standard linear equation $y=mx+c$ .we get $m=-1$ .

Hence, slope of CD (m)= -1

Now, the equation of line CD passing through (0,1) is given by :-

$(y-1)=m(x-0)\\\Rightarrow(y-1)=(-1)x\\\Rightarrow x+y=1$

Thus, the equation of line CD = $x+y=1$

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Question 3)

Given

The point (1, -5)

The slope m = -5/6

Using the point-slope form of the equation of a line

$y-y_1=m\left(x-x_1\right)$

where

m is the slope of the line

(x₁, y₁) is the point

In our case:

m = -5/6

(x₁, y₁) = (1, -5)

substituting the values m = -5/6 and the point (1, -5) in the point-slope form of the equation of the line

$y-y_1=m\left(x-x_1\right)$

$y-\left(-5\right)=-\frac{5}{6}\left(x-1\right)$

$y+5=-\frac{5}{6}\left(x-1\right)$

Thus, the point-slope form of the equation of the line is:

$y+5=-\frac{5}{6}\left(x-1\right)$

Question 4)

Given

The point (-1, 5)

The slope m = -7/2

In our case:

m = -7/2

(x₁, y₁) = (-1, 5)

substituting the values m = -7/2 and the point (-1, 5) in the point-slope form of the equation of the line

$y-y_1=m\left(x-x_1\right)$

$y-5=-\frac{7}{2}\left(x-\left(-1\right)\right)$

$y-5=-\frac{7}{2}\left(x+1\right)$

Thus, the point-slope form of the equation of the line is:

$y-5=-\frac{7}{2}\left(x+1\right)$

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