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Find an equation of the line.Write the equation in the standard form.

Through (7,3)​; parallel to 8x−y=9.

1 Answer

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As the line is parallel to the given line, the slopes of both lines are equal.

The given line 8x − y = 9 can be written in slope-intercept form as:

y = 8x - 9

Comparing with y = mx + b, we get slope m = 8.

Therefore, the slope of the line we need to find is also 8.

Using the point-slope form of the equation of a line, we have:

y - y1 = m(x - x1)

where (x1, y1) = (7, 3) and m = 8.

Substituting the values, we get:

y - 3 = 8(x - 7)

y - 3 = 8x - 56

y = 8x - 53

This is the equation of the line in slope-intercept form. To convert it to standard form, we move all the variables to the left-hand side:

-8x + y = -53

Therefore, the equation of the line in standard form is:

8x - y = 53.
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