To find the equation of a line given in the slope-intercept form y = mx + b, where m represents the slope of the line and b represents the y-intercept, we can use the provided information:
Given:
y = -2/3x + [ ? ]
From the given equation, we can identify:
m (slope) = -2/3
b (y-intercept) = ?
Therefore, the equation of the line in slope-intercept form is:
y = -2/3x + b
To find the y-intercept (b), we look for the value where the line intersects the y-axis, which is the point (0, b).
Since the y-intercept is the value of y when x = 0, we substitute x = 0 into the equation:
y = -2/3(0) + b
y = 0 + b
y = b
Therefore, the equation of the line is:
y = -2/3x + b
In this case, the y-intercept (b) is the point where the line intersects the y-axis, and it is represented by the value that replaces the question mark in the given equation.
