All Intermediate Geometry Resources
Example Questions
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 forto find the slope:
Addto each side of the equation:
Divide each side of the equation by:
Substituting the value ofback into the slope-intercept equation, we get:
By subtractingon 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 ofwhen.
So we first setto zero.
turns into
Lets subtract两边移动to one side of the equation.
After doing the arithmetic, we have
.
Divide byfrom both sides
Example Question #1 :How To Find The Equation Of A Curve
What is the-intercept of:
To find the y-intercept, we set
So
turns into
.
After doing the arithmetic we get
.
Example Question #1 :How To Find The Equation Of A Curve
What is the-intercept of:
The x-intercept can be found where
So
turns into
.
Lets subtractfrom 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 isand-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 ofandinto 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 haveandas 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 #1 :How To Find The Equation Of A Curve
Which equation would have an x-intercept atand a y-intercept at?
We're writing the equation for a line passing through the pointsand. 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 interceptsand
The line will eventually be in the formwhereis the y-intercept.
The y-intercept in this case is.
To find the equation, plug infor, and the other point,as x and y:
addto 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-interceptsand?