Question 1205839: Given the equation 4x-2y=12
What is the slope of this line?
What is the y-intercept?
What is the x-intercept?
Any line parallel to this line will have a slope of.
Any line perpendicular to this line will have a slope of.
Determine if the ordered pair (1,-1) is a solution for the equation x-y=0.
Find the equation of the line containing the points (2,6) and (5,4).
Find the equation of the line passing through (7,8) and has an undfined slope.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! equation is 4x - 2y = 12
convert to slope intercept form as follows:
start with 4x - 2y = 12
add 2y to both sides and subtract 12 from both sides to get 4x - 12 = 2y
divide both sides by 2 to get 2x - 6 = y
flip sides to get y = 2x - 6.
that's the slope intercept form.
the slope is 2 and the y intercept is -6.
to find the x-intercept, set y = 0 to get 0 = 2x - 6
add 6 t0 both sides to get 6 = 2x
solve for x to get x = 3
you have:
slope = 2
y-intercept = -6
x-intercept = 3
line looks like this:
all lines parallel to this line will have the same slope of 2.
all lines perpendicular to this line will have a slope that is a negative reciprocal of 2 which is equal to -1/2.
if (1,-1) is on the line, then replacing x with 1 and y with -1 will make the equation true.
start with x - y = 0
replace x with 1 and y with -1 to get 1 - -1 = 0
this becomes 1 + 1 = 0 which becomes 2 = 0 which is not true.
the point (1,-1) is not on the line.
here's what it looks like.
the two points are (2,6) and (5,4)
the slope is (4 - 6) / (5 - 2) = -2/3
the equation becomes y = -2/3 + b
b is the y-intercept
solve for b by replacing x and y with their respective values from one of the points on the line.
one point is (2,6)
y = -2/3 * x + b becomes 6 = -2/3 * 2 + b
solve for b to get b = 6 + 4/3 = 7 and 1/3 = 7.333 rounded to 3 decimal places.
the equation is y = -2/3 * x + 22/3
the x intercept is the value of x when y is equal to 0.
start with y = -2/3 * x + 22/3
replace y with 0 to get 0 = -2/3 * x + 22/3
add 2/3 * x to both sides to get 2/3 * x = 22/3
multiply both sides by 3/2 to get x = 11.
the equation is y = -2/3 * x + 22/3
the y-intercept is 22/3
the slope is -2/3
the x-intercept is 11
here's the graph.
if the slope is undefined, then a division by 0 must have occurred.
slope is change in y divided by change in x.
if the value of y changes and the value of x doesn't change, then the change in the value of x will be 0 and the slope will be undefined.
the value of y can change to any value other than 8.
the value of x will remain at 7.
any value divided by 0 is undefined.
what you get is a vertical line.
the equation for a vertical line through the point (7,8) is x = 7.
the value of y = 8 is on that line as is any other value of y that is real and whose x-coordinate has a value of 7.
here's what the graph looks like.
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