All Intermediate Geometry Resources
Example Question #1 : How To Find The Equation Of A Curve
If a line's -intercept is . and the -intercept is , what is the equation of the line?
Write the equation in slope-intercept form:
We were given the -intercept, , which means :
Given the -intercept is , the point existing on the line is . Substitute this point into the slope-intercept equation and then solve for to find the slope:
Add to each side of the equation:
Divide each side of the equation by :
Substituting the value of back into the slope-intercept equation, we get:
By subtracting on both sides, we can rearrange the equation to put it into standard form:
Example Question #2 : How To Find The Equation Of A Curve
Find the -intercept of:
To find the x-intercept, we need to find the value of when .
So we first set to zero.
Lets subtract from both sides to move to one side of the equation.
After doing the arithmetic, we have
Divide by from both sides
Example Question #3 : How To Find The Equation Of A Curve
What is the -intercept of:
To find the y-intercept, we set
After doing the arithmetic we get
Example Question #4 : How To Find The Equation Of A Curve
What is the -intercept of:
The x-intercept can be found where
Lets subtract from both sides to solve for .
After doing the arithmetic we have
Divide both sides by
Example Question #5 : How To Find The Equation Of A Curve
Suppose two intercepts create a line. If the -intercept is and -intercept is , what is the equation of the line?
Rewrite the intercepts in terms of points.
X-intercept of 1: .
Y-intercept of 2:
Write the slope-intercept form for linear equations.
Substititute the y-intercept into the slope-intercept equation.
Substitute both the x-intercept point and the y-intercept into the equation to solve for slope.
Rewrite by substituting the values of and into the y-intercept form.
Example Question #6 : How To Find The Equation Of A Curve
Which equation has a y-intercept at 2 and x-intercepts at -1 and 6?
In order for the equation to have x-intercepts at -1 and 6, it must have and as factors. This leaves us with only 2 choices, or
This equation must also have a y-intercept of 2. This means that plugging in 0 for x will gives us a y-value of 2. Because we have two options, we could plug in 0 for x in each to see which gives us an answer of 2:
a) we can eliminate that choice
b) this must be the right choice.
If we hadn't been given multiple options, we could have set up the following equation to figure out the third factor:
divide by -6
Example Question #7 : How To Find The Equation Of A Curve
Which equation would have an x-intercept at and a y-intercept at ?
We're writing the equation for a line passing through the points and . Since we already know the y-intercept, we can figure out the slope of this line and then write a slope-intercept equation.
To determine the slope, divide the change in y by the change in x:
The equation for this line would be .
Example Question #8 : How To Find The Equation Of A Curve
Write the equation of a line with intercepts and
The line will eventually be in the form where is the y-intercept.
The y-intercept in this case is .
To find the equation, plug in for , and the other point, as x and y:
add to both sides
This means the equation is
Example Question #9 : How To Find The Equation Of A Curve
Which equation has the x- and y-intercepts and ?