Question 365461: Graph the line that is perpendicular to the graph of 7x+10y=4.5 and intersects that graph at its x-intercept. Found 2 solutions by ewatrrr, Theo:Answer by ewatrrr(24785) (Show Source):
Hi,
***General point-slope from of an equation is
y = mx + b where m is the slope and b is the value of y where the line crosses the y-axis
7x+10y=4.5
y = (-7/10)x + 4.5/10
0 = (-7/10)x + 4.5/10 x-intercept is when y = 0
x-intercept = (9/14)
Slope of the new line 1s 10/7
( perpendicular lines have slopes that are negativie reciprocals of one another)
10/7 is the negative reciprocal of -7/10
y = (10/7)x + b
Using ordered pair ((9/14),0) to solve for b
.918 = b
y = (10/7)x + .918
subtract 7x from both sides of the equation to get:
10y = -7x + 4.5
divide both sides of the equation by 10 to get:
y = .7x + .45
now you have the equation in slope intercept form.
a graph of this equation would look like this:
you want your line to be perpendicular to this line, so the slope of your new line has to be the negative reciprocal of the slope of the original line.
the slope of your original line is -.7
to get the negative reciprocal of -.7, first multiply it by -1 to get:
.7
then divide it into 1 to get:
1 / .7 which results in 1.428571429
that is the slope of your new line.
put that in the slope intercept form of the equation of y = mx + b to get:
y = 1.428571429 + b
all you need to do now is find b, which is the y intercept.
the problem states that your perpendicular line has to intersect with the original line at the x intercept of the original line.
the equation of your original line is y = -.7*x + .45
to find the x intercept of that equation, set y = 0 to get:
0 = -.7*x + .45
subtract .45 from both sides of that equation to get:
-.7x = -.45
divide both sides of this equation by -.7 to get:
x = .6428571143
you can see from the graph shown above, that the graph crosses the x axis at approximately that point.
you now have the point where the original graph crosses the x axis.
that point also needs to be the intersection of the line that will be perpendicular to the original line.
the point of intersection is therefore equal to (x,y) = (.642857143,0).
this is a common point to both equations.
we can use that point to find the y intercept of the perpendicular equation.
the perpendicular equation is y = 1.428571429*x + b
we substitute .642857143 for x and 0 for y to get:
0 = 1.428571429*.642857143 + b
we simplify this equation to get:
0 = .918367347 + b
we subtract .918367347 from both sides of this equation to get:
b = -.918367347
we put that value into the perpendicular line equation to get:
y = 1.428571429*x - .642857143
we graph that equation plus the original equation to get what is shown below:
we have a line that is perpendicular to the original line and intersect the original line at the x intercept of the original line.
