as you already know, the equation y=-7/4x-2, is already in slope-intercept form and thus its slope is the coefficient of the "x", namely -7/4.
parallel lines have the same exact slope, so a parallel line to this one will also have a slope of -7/4, and it passes through 4,2,
[tex] \bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad \qquad \qquad
slope = m\implies -\cfrac{7}{4}
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=-\cfrac{7}{4}(x-4)
\\\\\\
y-2=-\cfrac{7}{4}x+7\implies y=-\cfrac{7}{4}x+9 [/tex]
The equation of the line that is parallel to the line y=-7/4x-2 is y=-7/4x + 9 if the line passes through the point (4,2)
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a line:
y=-7/4x-2
As we know if two lines are parallel, then the slope of the lines will be equal.
The equation of the line that is parallel to the line y=-7/4x-2
y=-7/4x + c
Plug (4, 2) in the above line.
2 = (-7/4)4 + c
c = 9
y=-7/4x + 9
Thus, the equation of the line that is parallel to the line y=-7/4x-2 is y=-7/4x + 9 if the line passes through the point (4,2)
Learn more about the linear equation here:
brainly.com/question/11897796
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