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What is the equation of the line parallel to
3x + 2y = 8 and passes through the point
(4, -3)?

(4,-3)=1,x+y so easy broooooo

The equation of the line which is parallel to3x + 2y = 8 and passes through the point (4, -3) is y = -1.5x  + 3

Parallel lines have same slope, since slope is like measure of steepness and since parallel lines are of same steepness, thus, are of same slope.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

[tex]y = mx +c[/tex]

Let the straight line parallel to the line [tex]3x + 2y = 8[/tex] be [tex]y = mx +c[/tex]

Converting first line in slope intercept form, we get:

[tex]3x + 2y = 8\\\\y = -\dfrac{3x}{2} + 4\\\\y = -1.5x + 4[/tex]

Thus, the slope of the first line is -1.5

The second line being parallel to this, will have same slope. Thus, we get[tex]m = -1.5[/tex]

Thus, the equation of the second line is;

[tex]y = -1.5x +c[/tex]

Now, since it passes through (4,-3), therefore, putting x = 4 and y = -3 should satisfy the equation.

Thus, we get:

[tex]y = -1.5x +c\\\-3 = -1.5(4) + c\\c = 6-3 = 3[/tex]

Thus, the y-intercept of this line is c = 3

Thus, the equation of the second line is: y = -1.5x  + 3

Thus, the equation of the line which is parallel to3x + 2y = 8 and passes through the point (4, -3) is [tex]y = -1.5x + 3[/tex]

The graph of this equation is given below.

Learn more about parallel lines here:

https://brainly.com/question/13857011

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have a nice Thursday!