The coefficient of x is the slope of the parallel line, option (C) m=3 is the correct answer.
What is slope of a line?
The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the above situation,
The equation is y = 3x - 2.
The general form of equation for slope intercept form is [tex]y = mx + b[/tex]
Now compare the given equation with the general equation,
⇒ [tex]m=3[/tex].
Since the lines are parallel, the slope will be the same for all lines.
So, slope for the parallel line is also m = 3.
Now the equation in slope-intercept form that intersects the point (3,5) is
⇒ [tex]y - y1 = m(x-x1)[/tex]
⇒ [tex]y - 5 = 3(x-3)[/tex]
⇒ [tex]y-5=3x-9[/tex]
⇒ [tex]y=3x-9+5[/tex]
⇒ [tex]y=3x-4[/tex]
Hence we can conclude that the coefficient of x is the slope of the parallel line, option (C) m=3 is the correct answer.
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