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Point-slope form review

Review point-slope form and how to use it to solve problems.

What is point-slope form?

Point-slope is a specific form of linear equations in two variables:
yb=m(xa)
When an equation is written in this form, m gives the slope of the line and (a,b) is a point the line passes through.
This form is derived from the slope formula.
Want to learn more about point-slope form? Check out this video.

Finding point-slope equation from features or graph

Example 1: Equation from slope and point

Suppose we want to find the equation of the line that passes through (1,5) and whose slope is 2. Well, we simply plug m=2, a=1, and b=5 into point-slope form!
y5=2(x1)

Example 2: Equation from two points

Suppose we want to find the line that passes through the points (1,4) and (6,19). First, we use the two points to find the slope:
Slope=19461 =155=3
Now we use one of the points, let's take (1,4), and write the equation in point-slope:
y4=3(x1)
Problem 1
Write the point-slope equation of the line that passes through (7,3) whose slope is 2.

Want to try more problems like this? Check out this exercise.

Finding features and graph from point-slope equation

When we have a linear equation in point-slope form, we can quickly find the slope of the corresponding line and a point it passes through. This also allows us to graph it.
Consider the equation y1=2(x3). We can tell that the corresponding line passes through (3,1) and has a slope of 2. Now we can graph the line:
A first quadrant coordinate plane. The x- and y-axes each scale by one. The equation y minus one equals two times the difference of x minus three is graphed and labeled. The points three, one and four, three are plotted. There is a horizontal segment from three, one to four, one that is labeled plus one. There is a vertical segment from four, one to four, three that is labeled plus two.
Problem 1
What is the slope of the line y5=4(x8)?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
The line passes through which point?
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