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Example Questions
Example Question #231 : Algebra
Give the equation, in standard form, of the line on the above set of coordinate axes.
The
-intercept of the line can be seen to be at the point five units above the origin, which is . The -intercept is at the point three units to the right of the origin, which is . From these intercepts, we can find slope by setting in the formula
The slope is
Now, we can find the slope-intercept form of the line
By setting
, :
The standard form of a linear equation in two variables is
,
so in order to find the equation in this form, first, add
to both sides:
We can eliminate the fraction by multiplying both sides by 3:
Distribute by multiplying:
,
the correct equation.
Example Question #232 : Algebra
Write the given equation in standard form:
The equation in standard form is:
Simplify the right side by distribution.
Subtract
on both sides.
The equation becomes:
Subtract 3 from both sides.
The answer is:
Example Question #233 : Algebra
Given the point
with a slope of two, write the equation in standard form.
We will first need to write the point-slope form to set up the equation.
Substitute the slope and point.
Simplify the right side.
Add 3 on both sides.
Subtract
on both sides.
The answer is:
Example Question #12 : Standard Form
Find the equation in standard form:
Distribute the right side.
Subtract
on both sides.
The answer is:
Example Question #234 : Algebra
Rewrite the equation in standard form:
The standard form of a linear equation is:
Multiply by two on both sides to eliminate the fraction.
Subtract
on both sides.
Subtract 6 from both sides.
The answer is:
Example Question #11 : Standard Form
Given the slope is 3, and the y-intercept is 6, write the equation of the line in standard form.
The standard form of a line is:
First, we can write the equation in slope-intercept form:
Subtract
on both sides.
The answer is:
Example Question #235 : Algebra
Given the slope of a line is 7, and a known point is (2,5), what is the equation of the line in standard form?
The standard form of a line is:
We can use the point-slope form of a line since we are only given the slope and a point.
Substitute the slope and the point.
Simplify this equation.
Add
on both sides.
Subtract
from both sides.
Simplify both sides.
The answer is:
Example Question #61 : Linear Algebra
Rewrite the equation in standard form:
Distribute the four through both terms of the binomial.
Subtract
on both sides of the equation.
Simplify both sides.
The answer is:
Example Question #23 : Standard Form
Which of the following is an equation, in standard form, of the line of the coordinate plane with intercepts
and ?
First, find the slope-intercept form of the equation. This is
,
where
is the slope and is the -intercept of the line. Since is this intercept, . Also, the slope of a line with intercepts and is , so, setting ,.
The slope-intercept form is
The standard form of the equation is
,
where, by custom,
, , and are relatively prime integers, and . To accomplish this:Switch the expressions:
Add
to both sides:
Multiply both sides by 3 to eliminate the denominator and make the coefficients integers with GCF 1:
Distribute on the left:
This is the correct equation.
Example Question #236 : Algebra
Rewrite the equation
in standard form so that the coefficients are integers, the coefficient of
is positive, and the three integers are relatively prime.
The standard form of the equation of a line is
.
To rewrite the equation
in this form so that
has a positive coefficient, first, switch the places of the expressions:
Get the
term on the left and the constant on the right by adding to both sides:
To eliminate fractions and ensure that the coefficients are relatively prime, multiply both sides by lowest common denominator 14:
Multiply 14 by both expressions in the parentheses:
Cross-canceling:
,
the correct choice.
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