Answer:
Last option, y = -4/3x - 2/3
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
number that describes both the direction and the steepness of the line
slope = rise/run
b represents the y-intercept
point where crosses the y-axis
Given:
- line 3x - 4y = 2
- passes through the point (1, - 2)
Let change 3x - 4y = 2 into y = mx + b form,
3x - 4y = 2
subtract 3x from both sides,
3x - 3x - 4y = 2 - 3x
- 4y = 2 - 3x
divided both sides by -4 to get y alone,
- 4y / -4 = 2 - 3x / - 4
y = (3x / 4) - (2 / 4)
→ y = (3/4)x - (1/2)
Slope of perpendicular lines to another is the negative reciprocal
(ex. slope of 2 becomes -1/2)
So for y = (3/4)x - (1/2) the slope will be,
slope = -4/3
We need to find b (y-intercept),
we know it passes through point (1, - 2)
a point is (x, y) format
y = -(4/3)x + b
plug in the point (1, - 2),
-2 = -4/3(1) + b
-2 = -4/3 + b
add 4/3 to both sides to get b alone,
-2 + 4/3 = -4/3 + 4/3 + b
-2/3 = b
the perpendicular line equation is,
y = -4/3x - 2/3
Learn more about slope and y-intercept here: brainly.com/question/12763756
