To find the equation of a line parallel to a given line, we can use the fact that parallel lines have the same slope.
First, let's determine the slope of the given line. We can rewrite the equation 8x - 9y = 7 in slope-intercept form (y = mx + b), where m is the slope.
8x - 9y = 7
-9y = -8x + 7
y = (8/9)x - 7/9
The slope of the given line is 8/9.
Since the line we want to find is parallel to the given line, it will also have a slope of 8/9.
Now we can use the point-slope form of a line (y - y₁ = m(x - x₁)) to find the equation of the line passing through the point (4, -5) with slope 8/9.
y - (-5) = (8/9)(x - 4)
y + 5 = (8/9)x - 32/9
To simplify, let's multiply both sides of the equation by 9 to eliminate the fraction:
9(y + 5) = 8x - 32
9y + 45 = 8x - 32
Now we can rewrite the equation in slope-intercept form:
9y = 8x - 32 - 45
9y = 8x - 77
y = (8/9)x - 77/9
Therefore, the equation of the line containing the given point (4, -5) and parallel to the given line 8x - 9y = 7 is y = (8/9)x - 77/9.
Write an equation of the line containing the given point and parallel to the given line.
(4, -5); 8x - 9y = 7
1 answer