 # Linear Algebra - Equation of the Line

## Question

1. Write the equation of the line that has the indicated slope and contains the indicated point. Express the final equation in standard form.
m = 3/5,(-1,4)

2. Write the equation of the line that has the indicated slope and contains the indicated point. Express the final equation in standard form.
m = 2; (−1, −2)

3. Write the equation of the line that has the indicated slope, m, and y intercept, b. Express the final equation in slope-intercept form.
m = − 7/9; b = 0

4. Write the equation of the line that contains the indicated pair of points. Express the final equation in standard form.
(4, 5) and (9, 8)

5. Write the equation of the line that contains the indicated pair of points. Express the final equation in standard form.
(−9, 5) and (7, −9)

6. Write the equation of the line that satisfies the given conditions. Express the final equation in standard form.
Contains the point (−5, 7) and is perpendicular to the line x − 3y = 5

## Solution Preview

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Write the equation of the line that has the indicated slope and contains the indicated point. Express the final equation in standard form.
m = 3/5,(-1,4)
Solution: Standard form is Ax + By = C. Slope Intercept form is y=mx+b where m is the slope. So, we have that m=3/5. If we put the coordinate of the point in slope intercept form we get:
4=-1*3/5+b, and hence b=4+3/5 or b=23/5.
Now, we have that y=(3/5)*x+(23/5) or 5y=3x+23 or , in the standard form, -3x+5y=23....

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