Question

How do you the equation of the line that passes through point (-3,2) and is parallel to the line formed by the equation y = 4x + 7?
need it urgently please , thanks​

Answer 1

Answer:

$\boldsymbol{y=4x+14}$

Step-by-step explanation:

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PART 1

First of all we need to find, the slope of the line that is parallel to the line $\boldsymbol{y=4x+7}$. Which is pretty easy, considering the fact that the slopes of parallel lines are the same.

The slope of the line $\boldsymbol{y=4x+7}$ is $\boldsymbol 4$.

Which means the slope of the line that is parallel to the one above is also 4.

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PART 2

Now we should find the equation of the line. We know that its slope is 4, so let's stick in 4 for the slope into the slope-intercept form equation:

(remember, m denotes the slope and b denotes the y intercept).

$\boldsymbol{y=mx+b}$

Stick in 4 for the slope.

$\boldsymbol{y=4x+b}$

Note that we are also given a point that's on the line.

We can stick in its y-co-ordinate, 2. for y.

$\boldsymbol{2=4x+b}$

Now let's stick in -3 for x.

$\boldsymbol{2=4(-3)+b}$

Solve for b.

$\boldsymbol{2=-12+b}$

Add 12 to both sides.

$\boldsymbol{2+12=b}$

$\boldsymbol{14=b}$

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Now that we know the y-intercept, let's stick it into the slope-intercept form equation for b:

$\boldsymbol{y=4x+14}$. Which is our final answer, the equation.

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Answer 2

Answer:

y = 4x + 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x + 7 ← is in slope- intercept form

with slope m = 4

• Parallel lines have equal slopes , then

y = 4x + c ← is the partial equation

to find c substitute (- 3, 2 ) into the partial equation

2 = - 12 + c ⇒ c = 2 + 12 = 14

y = 4x + 14 ← equation of parallel line