Write an equation that has a slope of -2/3 in Point-slope form and Slope-intercept form.
To write an equation with a slope of -2/3 in point-slope form, we need to have the slope and one point on the line. Let's say we have the point (x₁, y₁).
Point-slope form: y - y₁ = m(x - x₁)
Since the slope is -2/3, we replace m with -2/3:
y - y₁ = (-2/3)(x - x₁)
Now, let's write the equation in slope-intercept form. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
To convert the equation from point-slope form to slope-intercept form, we need to isolate y.
Starting with the equation in point-slope form:
y - y₁ = (-2/3)(x - x₁)
Distribute -2/3 to (x - x₁):
y - y₁ = (-2/3)x + (2/3)x₁
Now, let's isolate y by moving -y₁ to the other side:
y = (-2/3)x + (2/3)x₁ + y₁
The equation in slope-intercept form is:
y = (-2/3)x + (2/3)x₁ + y₁