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4 years ago

What is the equation, in slope-intercept form, of the line that is perpendicular to the line

Mathematics

1 answer:

Vadim26 [7]4 years ago

4 0

Answer:

y = -x-4

Step-by-step explanation:

In this question, we want to find the equation of a line.

Generally, the equation of a starlight line goes by the firm y = mx + c where m represents the slope and c represents the y-intercept

The first equation given, can be rewritten as ;

y = x -6 + 4

y = x - 2

From here, it is clear that our slope m is equal to 1.

Now if two lines are perpendicular, the product of their slopes equals -1

what i’m saying is m1•m2 = -1

Now since we know both lines are perpendicular, then we have the slope of the second line as -1 in value

Now after getting the slope, we need to write the equation using that point that falls on where the line passes through

Using;

y = mx + c for slope -1 and point (-2,-2)

we have;

-2 = -1(-2) + c

-2 = 2 + c

c = -2-2

c = -4

Thus our final equation is where we are having m to be -1 and c = -4

y = -1(x) -4

y = -x-4

ps : different equations in the note and on the screenshot. I followed what’s in the question!

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4 years ago

Factor: a) 4x^2-13x+9

Fittoniya [83]

Answer:

A. $x = \frac{9}{4}$

B. $x = 1$

Step-by-step explanation:

I don't know if you know this method. I'll explain.

1. Rewrite the same expression, but multiplied and divided by the same number that has the squared variable.

$4(\frac{4x^2-13x+9}{4})$

2. Take this expression to the expression $x^{2} +bx+c$ , you can do this by grouping. (4)( $4x^{2}$ ) can be grouped as $(4x)^2$ ; since what we want is to keep the (4x) in parenthesis, we don't multiply by 13. leaving it like 13(4x). Finally, we multiply 4 * 9 = 36. The denominator remains. Leaving the expression like:

$\frac{(4x)^2-13(4x)+36}{4}$

So you see, we now have the expression $x^2+bx+c$

$x^{2} =(4x)^{2}$

$bx = -13(4x)$

$c = 36$

3. Solve the expression by making 2 parenthesis, extracting (4x) and putting it into both of them like so.

(4x) (4x)

The sign in the first parenthesis is going to be the same as the second number; in this case, negative.

(4x -) (4x)

The sign in the second parenthesis is going to be the multiplication of the second and third signs in front of the numbers. In this case (-) (+) = -

(4x -) (4x -)

Next, we have to find a number that multiplied by another number be equal to ''c'' and added up or substracted (depending on the signs) be equal to ''b''. In this case, since we have the same signs in both parenthesis, we must only find a number which multiplied by another number be equal to 36 and substracted by that number be equal to 13. These two numbers are: 9 and 4 because 9 * 4 = 36 and - 9 + (-4) = -13

Remember that everything is being divided by 4 in this problem.

$\frac{(4x-9)(4x-4)}{4}$

4. Factor. If you have done everything correctly, the factor number will be the same as the one in the denominator. In this case, it's 4.

$(4x-4)$ is factorable. Their common factor number is 4. If you do not remember how to factor, it's basically dividing by a common number or variable.