Write the equation of each line using the given information.
1 answer:
Answer:
a. 10x + 2y = 23
b. 4x - y + 3 = 0
c. y + 8 = 0
d. 2x - y + 4 = 0
Step-by-step explanation:
a.
Slope of the line 'm' is =
= -5
Equation of the line with slope m and passing through the point (x₁,y₁) is y-y₁ = m·(x-x₁)
⇒y-1.5 = -5·(x-2)
⇒y = -5x + 10 + 1.5
⇒<u>5x + y = 11.5</u> (or) <u>10x + 2y = 23</u>
b.
Slope of the line 'm' = 4
Equation of the line with slope m and passing through the point (x₁,y₁) is y-y₁ = m·(x-x₁)
⇒y-15 = 4·(x-3)
⇒y = 4x -12 + 15
⇒<u>4x - y + 3 = 0</u>
c.
Line is parallel to y = 1
Equations of parallel lines only differ by constant. So the required line equation has the form y = c where c is any real number.
But, it is given that the line passes through the point (3,-8)
⇒c=-8
⇒<u>y = -8</u> (or) <u>y + 8 = 0</u>
d.
Equation of a line with slope 'm' and y-intercept of (0,c) is of the form y = mx + c
⇒y = 2x + 4
⇒<u>2x - y + 4 = 0</u>
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Answer:
Step-by-step explanation:
To write a quadratic equation into binomial form we can compare the equation into the completing square form of a quadratic equation like this ,
now since,
we can equate both the equations from left hand side to right hand side like this,
now we solve,
now we compare the coefficients of x^2:
now we compare the coefficients of x :
now we compare the constants , (constants are the letters which are not associated with any variable in this case the variable is x)
so now the value we got all the values for the completing square form we plug those in , a = 1 , h = -12 , k = 0 ,
this is the square of a binomial, if you want to verify if we expands this formula by the formula of (a + b)^2 we would get the same result. Thus this is the correct answer.