The equation of the line which is parallel to3x + 2y = 8 and passes through the point (4, -3) is y = -1.5x + 3
How are parallel straight lines related?
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.
How to get the slope intercept form of a straight line equation?
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.
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