How do you write the equation for the line (-14, -5) and parallel to the line determined by #6x + 7y = 28#?

Question

Nathan Axel · Accepted Answer

#y=-6/7x-17# #• " Parallel lines have equal slopes"# #"the equation of a line in "color(blue)"slope-intercept form"# is. #•color(white)(x)y=mx+b# #"where m is the slope and b the y-intercept"# #"rearrange "6x+7y=28" into this form"# #"subtract "6x" from both sides"# #7y=-6x+28# #"divide all terms by 7"# #y=-6/7x+4larrcolor(blue)"in slope-intercept form"# #"with slope "=-6/7# #y=-6/7x+blarrcolor(blue)"is the partial equation"# #"to find b substitute "(-14,-5)" into the partial equation"# #-5=12+brArrb=-5-12=-17# #y=-6/7x-17larrcolor(red)"is equation of line"#

Kennedy Adams · Answer

undefined To find the equation of a line parallel to a given line, we first need to determine the slope of the given line. The equation of the given line is in the form Ax + By = C, where A, B, and C are constants.

To find the slope of the given line, we rearrange the equation into slope-intercept form (y = mx + b), where m is the slope:

$$ 6x + 7y = 28 $$
$$ 7y = -6x + 28 $$
$$ y = -\frac{6}{7}x + 4 $$

Therefore, the slope of the given line is -6/7.

Since parallel lines have the same slope, the slope of the line we want to find is also -6/7.

Now, we use the point-slope form of the equation of a line to find the equation of the line passing through the point (-14, -5) with slope -6/7:

$$ y - y_1 = m(x - x_1) $$

Substitute the point (-14, -5) and the slope -6/7 into the equation:

$$ y - (-5) = -\frac{6}{7}(x - (-14)) $$
$$ y + 5 = -\frac{6}{7}(x + 14) $$
$$ y + 5 = -\frac{6}{7}x - \frac{6}{7} \times 14 $$
$$ y + 5 = -\frac{6}{7}x - 12 $$
$$ y = -\frac{6}{7}x - 12 - 5 $$
$$ y = -\frac{6}{7}x - 17 $$

Therefore, the equation of the line parallel to 6x + 7y = 28 and passing through (-14, -5) is y = -6/7x - 17.

Hazel Anglin · Answer

undefined To write the equation for a line parallel to the line determined by 6x + 7y = 28, we need to use the fact that parallel lines have the same slope.

First, we need to find the slope of the line 6x + 7y = 28. We rearrange the equation into slope-intercept form (y = mx + b), where m is the slope:

6x + 7y = 28
7y = -6x + 28
y = (-6/7)x + 4

So, the slope of the given line is -6/7.

Now, since the parallel line has the same slope, we can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

Given the point (-14, -5) and the slope -6/7, we plug these values into the point-slope form:

y - (-5) = (-6/7)(x - (-14))

Simplify:

y + 5 = (-6/7)(x + 14)

This is the equation for the line parallel to the given line and passing through the point (-14, -5).