Question #ecc2a

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Question #ecc2a

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Answer 1 · 2017-12-07T10:49:19

$y = 5 x + 6$ $y=5x+6$

Explanation:

$∙ parallel lines have equal slopes$ $• " parallel lines have equal slopes"$

$the equation of a line in slope-intercept form$ $"the equation of a line in "color(blue)"slope-intercept form"$ is.

$∙ x y = m x + b$ $•color(white)(x)y=mx+b$

$where m is the slope and b the y-intercept$ $"where m is the slope and b the y-intercept"$

$y = 5 x - 3 is in this form$ $y=5x-3" is in this form"$

$with m = 5$ $"with "m=5$

$\Rightarrow y = 5 x + b \leftarrow is the partial equation$ $rArry=5x+blarrcolor(blue)"is the partial equation"$

$to find b substitute (- 2, - 4)$ $"to find b substitute "(-2,-4)$
$into the partial equation$ $"into the partial equation"$

$- 4 = - 10 + b \Rightarrow b = - 4 + 10 = 6$ $-4=-10+brArrb=-4+10=6$

$\Rightarrow y = 5 x + 6 is equation of parallel line$ $rArry=5x+6" is equation of parallel line"$

Answer 2 · 2017-12-07T10:49:39

The equation of the given line
$y = 5 x - 3$ $y=5x-3$

Since the line we are asked to find is parallel to the given line, their slope must be equal.

The slope of the given line $=$ $=$ The slope of the unknown line $= 5$ $=5$

( I hope you know how to find the slope using the equation of the line)

Now,
The unknown line also passes through $(- 2, - 4)$ $(-2,-4)$

Applying the Point-Slope Form,
$y - y_{1} = m (x - x_{1})$ $y-y_1 = m(x-x_1)$

where,
$(x_{1}, y_{1})$ $(x_1,y_1)$ are the coordinates of the point that lies on the line.

$(y + 4) = 5 (x + 2)$ $(y+4) = 5(x+2)$

$5 x - y + 6 = 0$ $5x -y +6=0$

Answer 3 · 2017-12-07T11:00:24

$y = 5 x + 6$ $y=5x+6$

Explanation:

If two line are parallel, then they have he same gradient:

Gradient of $y = 5 x - 3$ $y=5x-3$ is 5.

Equation of a line:

$y_{2} - y_{1} = m (x_{2} - x_{1})$ $y_2-y_1=m(x_2-x_1)$

Equation of line passing through point $(- 2, - 4)$ $( -2 , -4 )$

$y - (- 4) = 5 (x - (- 2)$ $y-(-4)=5(x-(-2)$

$y + 4 = 5 (x + 2)$ $y+4=5(x+2)$

$y + 4 = 5 x + 10$ $y+4=5x+10$

$y = 5 x + 6$ $y=5x+6$

Graph:

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