Question

A given line has the equation 10x+2y=−2 . What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?
a. y=−5x+12
b. 5x+y=12
c. y−12=5(x−0)
d. 5x+y=−1

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

A given line has the equation 10x + 2y = −2

TO CHOOSE THE CORRECT OPTION

The equation of the line in slope-intercept form that is parallel to the given line and passes through the point (0, 12) is

a. y = − 5x + 12

b. 5x + y = 12

c. y − 12 = 5(x−0)

d. 5x + y = −1

EVALUATION

The given equation of the line is

$\sf{10x + 2y = - 2}$

On simplification we get

$\sf{5x + y = - 1} \: \: \: \: \: ...(1)$

Now the equation of the line parallel to equation (1) is

$\sf{5x + y = k \: \: \: \: \: \: .......(2)}$

Now The equation (2) passes through the point (0,12)

So we get from equation (2)

$\sf{(5 \times 0) + 12 = k \: }$

$\implies \sf{k = 12 \: }$

Hence the equation (2) becomes

$\sf{5x + y = 12 \: }$

This equation can be rewritten as

$\sf{ y = - 5x + 12\: }$

Which is of the Slope - Intercept form

RESULT

The required equation of the line in slope-intercept form is

$\boxed{ \sf{a. \: \: \: \: \: \: \: \: y = - 5x + 12\: \: \: }}$

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LEARN MORE FROM BRAINLY

Draw the graph of the linear equation 2 x + 3 y = 12.

At what points, the graph of the equation cuts the X & Y axes?

https://brainly.in/question/23087776

Answer 2

Answer:

A

Step-by-step explanation: