1. x = a
2. y = b
3. A vertical line has an undefined slope.
4. rise/run or Change in y/change in x (m) = y2 - y1 / x2 - x1
5. Rewrite the equation in slope-intercept form to determine the y-intercept.
What is the Equation of a Line?
In slope-intercept form, the equation of a line in slope-intercept form is, y = mx + b, where m is the slope and the y-intercept = b.
1. The slope of a vertical line is undefined, therefore, the equation for a vertical line is given as: x = a, where a is the value of the x-intercept.
A vertical line that contains (a, b) will have the equation, x = a.
2. The slope of a horizontal line is 0, therefore, the equation of the horizontal line is, y = b, where b is the y-intercept.
A horizontal line that contains (a, b) will therefore have the equation, y = b.
3. A vertical line has an undefined slope.
4. For example, if we have the two points (3, 3) and (0, 5), two methods to find the slope are:
rise/run
or
Change in y/change in x (m) = y2 - y1 / x2 - x1 = 5 - 3 / 0 - 3 = 2/-3 = -2/3.
5. If we have an equation in point-slope form, for example, y - 3 = 2(x - 4), to find the coordinates of its y-intercept, rewrite the equation in slope-intercept form to determine the y-intercept:
y - 3 = 2x - 8
y = 2x - 8 + 3
y = 2x - 5
The y-intercept is -5, thus, the coordinates would be: (0, -5).
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