Respuesta :
Line passing through (0, 4) and (3, 0); slope = -4/3 and y-intercept is 4. Therefore the equation is given by [tex]y=- \frac{4}{3} x+4[/tex]
The correct answers are:
y = -4/3x + 4; undefined; and 40
Explanation:
The equation of a line can be represented in slope-intercept form, y=mx+b. The slope is represented as m and the y-intercept as b. The formula for slope is
m = (y₂-y₁)/(x₂-x₁)
Using our points, we have m = (0-4)/(3-0) = -4/3.
The y-intercept is where the data crosses the y-axis; this means it will have an x-coordinate of 0. This makes the first point our y-intercept. This gives us the equation y = -4/3x + 4.
The slope of a vertical line is undefined. This is because it is the change in y over the change in x; since the x-value does not change, this will be 0, which means we are dividing by 0, which is undefined.
The rate of change is the same thing as slope:
m = (y₂-y₁)/(x₂-x₁) = (220-100)/(3-0) = 120/3 = 40