To find the equation of a line perpendicular to the given line, we need to find the slope of the given line and then find the negative reciprocal of that slope.
First, let's find the slope of the given line: 8x + 7y = 9
To do this, let's put the equation in slope-intercept form (y = mx + b), where m is the slope:
7y = -8x + 9
y = (-8/7)x + 9/7
The slope of the given line is -8/7.
The negative reciprocal of -8/7 is 7/8.
Now, let's use the point (0,5) and the slope 7/8 to find the equation of the line using the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
(x1, y1) = (0, 5)
y - 5 = (7/8)(x - 0)
y - 5 = 7/8x
Finally, let's rearrange the equation to the slope-intercept form:
y = 7/8x + 5
Therefore, the equation of the line containing the point (0,5) and perpendicular to the line 8x + 7y = 9 is y = 7/8x + 5.
Write an equation of the line containing the given point and perpendicular to the given line.
(0,5); 8x + 7y = 9
1 answer