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3 years ago

what is the slope intercept form of a line that is perpendicular to y = x + 3 and passes through point (2, -4)

Mathematics

1 answer:

Assoli18 [71]3 years ago

3 0

Answer:

The equation of the perpendicular line is y = -x - 2

Step-by-step explanation:

* Lets revise the form of the slope intercept for

- The slope intercept form is y = mx + b, where m is the slope of

the line and b is the y-intercept

* Now lets revise the relation between the slopes of the

perpendicular lines

- If two lines are perpendicular, then the product of their slopes is -1

# Ex: If line L has slope m1 and line K has slope m2, and L ⊥ K

∴ m1 × m2 = -1

∴ m2 = -1/m1

* Now lets solve the problem

- We need to find the equation of the line which is perpendicular to

the line whose equation is y = x + 3 and passes through point (2 , -4)

- Find the slope of the given equation

∵ y = x + 3

- In this form the slope is the coefficient of x

∴ m = 1

- Find the slope of the perpendicular line

∵ The slope of the perpendicular line = -1/m

∴ The slope of it = -1/1 = -1

- Write the equation of the line with the value of the slope

∴ y = -x + b

- To find the value of b substitute x , y in the equation by the x and

y of the given point

∵ The line passes through point (2 , -4)

∵ y = -x + b

∴ -4 = -1(2) + b

∴ -4 = -2 + b ⇒ add 2 for both sides

∴ b = -2

- Write the equation with the value of b

∴ y = -x - 2

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Softa [21]

We have

1/2 liter apple juice ---- 1/3 of her glass

1-liter apple juice --- x

x is the number of glass filled with 1 liter

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

we can obtain equivalent fractions like

$\frac{2}{3}=\frac{4}{6}$

the answers are 2/3 and 4/6

6 0

1 year ago

Write the Slope-Intercept and Point-Slope forms of the line passing through the point (-3, 2) and having a slope of -4/5

weeeeeb [17]

Answer:

slope-intercept: $y=\frac{-4}{5} x-\frac{2}{5}$

point-slope: $y-2=\frac{-4}{5} (x+3)$

Step-by-step explanation:

The slope-intercept form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

The point-slope form of a line is written as y - y1 = m(x - x1), where (x1, y1) is a given point and m is the slope.

Here, we see that the slope is -4/5, which means that m = -4/5. Since we're given a point (-3, 2), let's go ahead and just write the point-slope form already. (x1, y1) = (-3, 2) so x1 = -3 and y1 = 2. Then:

y - y1 = m(x - x1)

y - 2 = (-4/5) * (x + 3)

$y-2=\frac{-4}{5} (x+3)$

Now, we want to find the slope-intercept form, so we need to figure out the y-intercept. Well, first, let's plug in what we know:

y = mx + b

y = (-4/5)x + b

Any point on this line will satisfy the above equation. Since (-3, 2) is on this line, if we plug -3 in for x and 2 in for y, the equation should hold true, so we can solve for b:

y = (-4/5)x + b

2 = (-4/5) * (-3) + b

2 = 12/5 + b

b = -2/5

So, the y-intercept is -2/5. Then the slope-intercept form is:

$y=\frac{-4}{5} x-\frac{2}{5}$

Thus, our two equations are:

slope-intercept: $y=\frac{-4}{5} x-\frac{2}{5}$

point-slope: $y-2=\frac{-4}{5} (x+3)$

8 0

2 years ago

Mai says that the equation 2x+2=x+1 has no solutions because the left side is double the right side. Do you agree with mai provi

attashe74 [19]

Answer: No, Mai needs to solve the problem.

Step-by-step explanation:

2x+2=x+1 - subtract 2 from both sides

2x=x-1 - subtract x from both sides

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6 0

3 years ago

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If twice a number is subtracted from 11, the result is 4 more than the number. What is the number?

Flauer [41]

Let the number = x.

So 2 times x subtracted from 11 is written as 11-2x

The result is 4 more than the number is written as 4 +x

Now you have 11-2x = 4 + x

We can now solve for x.

Add 2x to each side:

11 = 4 + 3x

Subtract 4 from each side:

7 = 3x

Divide both sides by 3:

x = 7/3

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3 years ago