We can also find the equation of a line when given the slope and any point (not the y-intercept), and there are two methods to do so. The following video will use a single example to show how to use both methods to find the equation of a line with a given slope and single point.
Video Source (09:40 mins) | Transcript
These are the two methods to finding the equation of a line when given a point and the slope:
- Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Use the m given in the problem, and the b that was just solved for, to create the equation y = mx + b.
- Point-slope form = \({\text{y}} {-} {\text{y}}_1 = {\text{m}}({\text{x}}-{\text{x}}_1)\), where \(({\text{x}}_1, {\text{y}}_1)\) is the point given and m is the slope given. The 'x' and the 'y' stay as variables.
Additional Resources
- Find the equation of the line that passes through the point (1, 4) and has a slope of 12.
- Find the equation of the line that passes through the point (1, 4) and has a slope of 2.
- Find the equation of the line that passes through the point (27, 4) and has a slope of \(\frac{-2}{9}\).
- Find the equation of the line that passes through the point \((-11, 2)\) and has a slope of \(\frac{-5}{11}\).
- Find the equation of the line that passes through the point (10, 6) and has a slope of \(\frac{1}{5}\). What is the y-intercept of the line?
- Find the equation of the line that passes through the point (3, 29) and has a slope of 6. What is the y-intercept of the line?
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Cameron T.
1 Expert Answer
Lorraine T. answered • 08/27/21
"Math and Science tutor for all ages"
Use y= mx + b to solve,
sub in the given values: 6 = (-1)(-3) + b
therefore b = 3
so the equation is y = -x + 3