Four tysm if you are answering ! write an equation

Ответ:

gen73

11.03.2022

Mathematics

17. Equation : y=-x-1

18: Equation: $y=\frac{1}{2}x+8$

19: Equation: y=3x-6

20: Equation: $y=\frac{1}{3}x-2$

Step-by-step explanation:

Using the Slope-Intercept Form for the following questions:

Equation of line: y=mx+b where m is the slope and b is the y-intercept.

17. A(3, -4), y=-x+8

First substitute the slope from the original line y=-x+8 (i.e. -1 in this case) into the equation of line.

y=(-1)x+b .....(1)

Now, substitute the given point A(3,-4) in the equation (1), we have;

$-4=(-1)\cdot (3)+b$

-4=-3+b

-4+3=b

∴ b=-1

Substitute the value of b=-1 in the Slope-Intercept form i.e, y=-x+(-1)

y=-x-1

Therefore, the equation of the line passing through the given point that is parallel to the given line is, y=-x-1 .

18. A(-6, 5) , $y=\frac{1}{2}x -7$

First substitute the slope from the original line $y=\frac{1}{2}x -7$ (i.e. $\frac{1}{2}$ in this case) into the equation of line.

$y=\frac{1}{2} x+b$ .....(1)

Now, substitute the given point A(-6, 5) in the equation (1), we have;

$5=\frac{1}{2} \cdot (-6)+b$

5=-3+b

5+3=b

∴ b=8

Substitute the value of b=8 in the Slope-Intercept form i.e, $y=\frac{1}{2}x+8$

$y=\frac{1}{2}x+8$

Therefore, the equation of the line passing through the given point that is parallel to the given line is, $y=\frac{1}{2}x+8$ .

19. A(2,0), y=3x-5

First substitute the slope from the original line y=3x-5 (i.e. 3 in this case) into the equation of line.

y=3x+b .....(1)

Now, substitute the given point A(2, 0) in the equation (1), we have;

$0=3\cdot (2)+b$

0=6+b

∴ b=-6

Substitute the value of b=-6 in the Slope-Intercept form i.e, y=3x+(-6)

y=3x-6

Therefore, the equation of the line passing through the given point that is parallel to the given line is, y=3x-6

20. A(3, -1), $y=\frac{1}{3}x+10$

First substitute the slope from the original line $y=\frac{1}{3}x +10$ (i.e. $\frac{1}{3}$ in this case) into the equation of line.

$y=\frac{1}{3} x+b$ .....(1)

Now, substitute the given point A(3, -1) in the equation (1), we have;

$-1=\frac{1}{3} \cdot (3)+b$

-1=1+b

-1-1=b

∴ b=-2

Substitute the value of b=-2 in the Slope-Intercept form i.e, $y=\frac{1}{3}x+(-2)$

$y=\frac{1}{3}x-2$

Therefore, the equation of the line passing through the given point that is parallel to the given line is, $y=\frac{1}{3}x-2$ .

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Four tysm if you are answering ! write an equation of the line passing through the given point that is parallel to the given line for the following: (i put a picture bc it’s easier for me and hopefully for you) you so so much

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