we know that
If two lines are parallel, then their slopes are the same
Step 1
Find the slope of the given line
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
in this problem we have
[tex](x1,y1)=(-5,-4)\\(x2,y2)=(0,-3)[/tex]
substitute in the formula
[tex]m=\frac{(-3+4)}{(0+5)}[/tex]
[tex]m=\frac{(1)}{(5)}[/tex]
[tex]m=\frac{1}{5}[/tex]
Step 2
Find the equation of the line
we know that
the equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{1}{5}[/tex]
[tex](x1,y1)=(-2,2)[/tex]
substitute
[tex]y-2=\frac{1}{5}(x+2)[/tex]
[tex]y=\frac{1}{5}x+\frac{2}{5}+2[/tex]
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
therefore
the answer is
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
The equation of the line passing through the point [tex](-2,2)[/tex] and parallel to the given line is [tex]\boxed{5y = x + 12}[/tex].
Explanation:
The equation of a line is a linear equation which states the relation between [tex]x[/tex] and [tex]y[/tex] coordinate variables is linear. The slope [tex]m[/tex] of a line passing through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is calculated as shown below.
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
If two lines are parallel then this means that their slopes are equal. Thus, the slope of the line parallel to it, has the same slope.
Substitute[tex](-5,-4)[/tex] for [tex](x_1,y_1)[/tex] and [tex](0, -3)[/tex] for [tex](x_2,y_2)[/tex] in [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] to obtain the slope of a line passing through the points [tex](-5,-4)[/tex] and [tex](0, -3)[/tex].
[tex]\boxed{\begin{aligned}m& =\frac{-3 + 4}{0+5} \\&= \frac{1}{5}\end{aligned}}[/tex]
Therefore, the slope of the line required is [tex]\dfrac{1}{5}[/tex].
The point slope formula for a line passing through point [tex](x_1,y_1)[/tex] and has a slope [tex]m[/tex] is as shown below.
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute [tex]-2[/tex] for [tex]x_1[/tex], [tex]2[/tex] for [tex]y_1[/tex] and [tex]\frac{1}{5}[/tex] for [tex]m[/tex] to obtain the equation of the line with slope [tex]m=\frac{1}{5}[/tex] and passing through the point [tex](-2,2)[/tex].
[tex]\boxed{\begin{aligned}(y-2)&=\dfrac{1}{5}(x+2)\\5 \cdot (y-2)& = x+2\\5y-10& = x+2\\5y& = x +12\end{aligned}}[/tex]
The equation of the line parallel to the given line and passing through [tex](-2,2)[/tex] is [tex]\boxed{5y=x+12}[/tex].
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Answer Details:
Grade: Middle School
Subject: Mathematics
Chapter: Lines and curves
Keywords: linear equations, slope, point, slope point form, parallel, lines, passing, coordinates, axis, intercepts.
