To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then take the negative reciprocal of that slope.
The equation of the given line is 4x + 9y = 2.
To find the slope of this line, we need to rearrange the equation in slope-intercept form (y = mx + b), where m is the slope:
4x + 9y = 2
9y = -4x + 2
y = (-4/9)x + 2/9
From this equation, we can see that the slope of the given line is -4/9.
The slope of a line perpendicular to this line is the negative reciprocal of -4/9. Therefore, the slope of the perpendicular line is 9/4.
Now, we know the slope of the perpendicular line and the given point (0, 8). We can use the point-slope form of a linear equation to write the equation of the line:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope of the line.
Substituting the values into the equation, we have:
y - 8 = (9/4)(x - 0)
y - 8 = (9/4)x
Rearranging the equation, we can write it in slope-intercept form:
y = (9/4)x + 8
Therefore, the equation of the line containing the point (0, 8) and perpendicular to the line 4x + 9y = 2 is y = (9/4)x + 8.
Write an equation of the line containing the given point and perpendicular to the given line.
(0,8); 4x + 9y = 2
1 answer