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Which equation represents a line that is parallel to y = -4x + 3 and passes through the point (-3, 2)?
a. y = -4X – 10
b. y = -4x + 2
c. y = -4x + 5
d. y = 1/4x - 7/2
e. y = 1/4x + 11/4

Respuesta :

Answer:

A

Step-by-step explanation:

The first thing we shall do here is to get the slope of the first line.

Mathematically, to get this, we shall compare the given equation with the general equation of a line

The general equation of a line is ;

y = mx + c

where m is the slope and c is the y intercept

By comparison, y = -4x + 3 has a slope of -4

Now, since we are going to form a second equation, we shall be needing the slope of the second equation too. By mathematical convention, the slope of two lines which are parallel to each other are equal.

So practically, what this means is that the slope of the second line too is -4

Using the slope point form, we can find the equation of the second line too;

Mathematically, that will be;

y-y1/x-x1 = m

Thus;

y-2/x-(-3) = -4

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

y-2 = -4(x + 3)

y-2 = -4x -12

y = -4x -12 + 2

y = -4x -10

abidemiokin

The equation of the line that passes through the points (-3, 2) and is parallel to the line y= -4x +3 is y+4x = -10

The standard equation of a line in point-slope form is expressed as:

[tex]y-y_0=m(x-x_0)[/tex]

m is the slope of the line

(x0, y0) is any point on the line

Given the equation y = -4x + 3 parallel to this line, the slope of the line m = 1/7

Substitute the slope and the point into the formula to have:

[tex]y-2=-4 (x+3)\\y-2 = -4x-12\\y+4x=-10[/tex]

Hence the equation of the line that passes through the points (-3, 2) and is parallel to the line y= -4x +3 is y+4x = -10

Learn more here: https://brainly.com/question/17003809

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