To start off writing the equation of a vertical line passing through a point:
1. Recall that a vertical line has an undefined slope.
2. Identify the x-coordinate of the given point, which represents the x-coordinate of the vertical line. In this case, the x-coordinate is 7.
3. The equation of a vertical line passing through a specific x-coordinate is simply x = c, where c represents the x-coordinate. So, the equation for the vertical line passing through (7,-3) would be x = 7.
To start off finding the equation for a line with an undefined slope passing through a given point:
1. Recall that a line with an undefined slope is a vertical line.
2. Identify the x-coordinate of the given point, which represents the x-coordinate of the vertical line. In this case, the x-coordinate is -1.
3. The equation for a vertical line passing through a specific x-coordinate is x = c, where c represents the x-coordinate. So, the equation for the line passing through (-1,-2) would be x = -1.
To find the equation in slope-intercept form (y = mx + b) for a line, you need the following information:
1. The slope (m) of the line.
2. The y-coordinate (y) and x-coordinate (x) of a point on the line.
3. Once you have the slope and a point, you can substitute the values into the equation y = mx + b and solve for the y-intercept (b).
The point-slope form of an equation of a line is:
y - y₁ = m(x - x₁)
In this form, the equation represents a line with:
- m as the slope of the line,
- (x₁, y₁) as a point on the line.
You can use this form to find the equation of a line given a known point and the slope. Remember to substitute the values of the slope and point into the equation.