SOLUTION: write the slope-intercept equation for the line that passes through (14, -2) and is perpendicular to 7x

SOLUTION: write the slope-intercept equation for the line that passes through (14, -2) and is perpendicular to 7x - 10y = 18 please show all of your work

Question 460008: write the slope-intercept equation for the line that passes through (14, -2) and is perpendicular to 7x - 10y = 18 please show all of your work
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
A line perpendicular to another line with have negative inverse slope.
The define original line is
7x - 10y = 18
Subtract 7x from both sides
-10y = -7x + 18
Divide both sides by -10
y = 7/10*x -18/10
This equation is in slope-intercept format
y = mx +b
m = 7/10
So, the perpendicular line will have slope
-10/7
.
y = -10/7*x + b
.
You need the line to go through the point (14,-2).
That means when x=14, y=-2
Substitute
that with what we already know
-2 = -10/7*(14) + b
We can cancel the 14 with the 7
-2 = -10(2) + b
-2 = -20 + b
Add 20 to both sides
18 = b
.
y = -10/7*x + 18
.
Always check your answer, so substitute x=14 and see what value of y you get.
y = -10/7*14 + 18
y = -20 + 18
y = -2
That's right.
.
A graph is always helpful. In this case, graph both equations to see if they're perpendicular by visual inspection (of course, you KNOW they're perpendicular because of the slopes)...

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