McGraw Hill Glencoe Algebra 1, 2012
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McGraw Hill Glencoe Algebra 1, 2012 View details
2. Writing Equations in Slope-Intercept Form
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Exercise 52 Page 231

We need to review what we know about the equation of a line.

See solution.

Practice makes perfect
Let's begin by reviewing what we know about the equation of a line. We know that it can be written in the slope-intercept form, as shown below.
In this equation, is the slope and is the intercept. Let's see how different pieces of information about the line can help us complete the equation with the values of and

Slope and intercept

If we are given the slope and the intercept, then we can just substitute them in the slope-intercept form and get the final equation. Let's say that we are given that the slope of a line is and the intercept is To write its equation, we can substitute and

Slope and a Point

If we are given the slope and a point that the line passes through, then we can begin by substituting with the slope. Next we can substitute the given point in the equation to find the value of Let's say that we are given that the slope of a line is and it passes through the point We can substitute first.
Now we can substitute the given point in this equation to find
Finally, we can complete our equation!

Two Points

If we are given two points that the line is passing through, then we can use the Slope Formula to find the slope first. Then we can substitute one of the points to find Let's say that we are given that a line passes through the points and
Now we can substitute in our equation.
To find we can substitute one of the points in this equation. Let's take
Finally, we can complete our equation!

Conclusion

As we can see, given different pieces of information about a line, we can write its equation.