Answer:
To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
For #2: (4,3) and the line equation 4x-5y=30
1) First, let's rewrite the given equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
4x - 5y = 30
-5y = -4x + 30
y = (4/5)x - 6
2) The given line has a slope of 4/5. To find the slope of the line perpendicular to it, we take the negative reciprocal of 4/5, which is -5/4.
3) Now, we can use the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the given point and m is the slope.
Using the point (4,3) and the slope -5/4, we have:
y - 3 = (-5/4)(x - 4)
4) Simplifying the equation, we can distribute -5/4 to (x - 4):
y - 3 = (-5/4)x + 5
5) Finally, let's rewrite the equation in slope-intercept form:
y = (-5/4)x + 8
Therefore, the equation of the line that passes through the point (4,3) and is perpendicular to the line 4x-5y=30 is y = (-5/4)x + 8.
Step-by-step explanation:
