Considering the definition of perpendicular line, the y-intercept of the line that is perpendicular to the line 7x+2y=14 and passes through the point (7,-6) is -8.
<h3>Linear equation</h3>
A linear equation o line can be expressed in the form y = mx + b
where
- x and y are coordinates of a point.
- m is the slope.
- b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
<h3>Perpendicular line</h3>
Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
<h3>Equation of perpendicular line in this case</h3>
In this case, the line is 7x+2y=14. Expressed in the form y = mx + b, you get:
2y= 14 - 7x
y= (-7x + 14)÷ 2
<u><em>y= -7/2x - 7</em></u>
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -7/2. So:
-7/2× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-7/2)
<u><em>slope perpendicular line= 2/7</em></u>
So, the perpendicular line has a form of: y= 2/7x + b
The line passes through the point (7,-6). Replacing in the expression for perpendicular line:
-6= 2/7× (7) + b
-6= 2 + b
-6 -2 = b
<u><em>-8= b</em></u>, being b the y-intercept of the line.
Finally, the y-intercept of the line that is perpendicular to the line 7x+2y=14 and passes through the point (7,-6) is -8.
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