The slope of a line is defined as the change in y divided by the change in x:
Given a point `(x_1,y_1)`, the change in y can be written as
And the change in x can be written as:
The equation of the line can then be written:
In `y-(-4)=-4(x-2)` the point `(x_1,y_1)` is equal to (2,-4) and the slope is equal to -4.
Therefore the line passes through the point (2,-4) and this point is the basis of this equation.
The slope intercept form is y=mx+b, where m is the slope and b is the y intercept. To write the slope intercept method, solve for y.
Thus the slope is -4 and the y intercept is 4.
The standard form of a line is: ax+by=c. Add 4x to both sides of (1).
To determine the x intercept, substitute 0 for y.
Thus the x intercept is 1.
The equation of the line y + 4 = -4*(x - 2) is in the point slope form. Rewriting the equation `(y+4)/(x - 2) = -4` . The slope of this line is -4 and it passes through the point (2, -4).
y + 4 = -4*(x - 2)
=> y + 4 = -4x + 8
=> y = -4x + 4
This is the equation in the slope-intercept form.
At the x-intercept the y-coordinate is 0.
0 = -4x + 4
=> x = 1
The x-intercept of the line is 1.