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Algebra 1

Course: Algebra 1>Unit 5

Lesson 6: Summary: Forms of two-variable linear equations

Forms of linear equations: FAQ

Where are linear equations used in the real world?

There are countless applications for linear equations in the real world! For example, engineers might use linear equations to study the relationships between different physical properties, like force and displacement. Economists might use linear equations to model supply and demand, or to predict future trends.

What is slope-intercept form?

Slope-intercept form is one way to write a linear equation. The form is $y=mx+b$, where $m$ is the slope of the line and $b$ is the $y$-intercept.

How can we graph a slope-intercept equation?

Start by finding the $y$-intercept, or the point where the line crosses the $y$-axis. Plot that point first. Then, use the slope to find other points on the line. Remember that slope is "rise over run" - if the slope is positive, the line will go up as it goes to the right, and if the slope is negative, the line will go down as it goes to the right.

How can we write an equation in slope-intercept form?

We need two pieces of information: the slope and the $y$-intercept. Once we have those, we substitute the values in for $m$ and $b$ in the equation $y=mx+b$.

What is point-slope form?

Point-slope form is another way to write a linear equation. The form is $y-{y}_{1}=m\left(x-{x}_{1}\right)$, where $m$ is the slope and $\left({x}_{1},{y}_{1}\right)$ is any point on the line.
Practice with our Point-slope form exercise.

What is standard form?

Standard form is yet another way to write a linear equation. The form is $Ax+By=C$, where $A$, $B$, and $C$ are constants.

Why might we rewrite a linear equation in a different form?

There are a few reasons we might choose to rewrite a linear equation in a different form. For example, if we're trying to graph the equation, slope-intercept form might be the easiest to work with. But if we're trying to solve a system of equations, standard form might be more useful. It really depends on the situation.

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