How to write the slope-intercept form of the equation of the line described; (-2,-1) parallel to y = (-3/2)x - 1?
Coordinate Geometry is a very important topic in mathematics in which various equations are represented as curves on the cartesian, polar, or other types of planes.
Answer: The slope-intercept form of the equation of the line passing through (-2,-1), and parallel to y = (-3/2)x - 1 is y = (-3/2)x - 4.
Let us observe the solution step by step.
Now, let us have a look at the slope-intercept form of the equation of a line.
Given: (x1, y1) = (-2, -1)
From the given equation of straight line y = (-3/2)x - 1
The slope-intercept form of a linear equation is y = mx + b; where m is the slope and b is the y-intercept value.
Hence, the slope of the given line is: m = −3 / 2
As we know that parallel lines have the same slope. Therefore, we can substitute this slope in the formula:
y = (-3 /2)x + b ------(1)
Since the line passes through the point (-2, -1), we can substitute in equation (1)
-1 = (-3/2) (-2) + b
-1 = 3 + b
b = -4
Now we can substitute the slope and y-intercept into the formula.
y = (-3/2)x + (-4)
y = (-3 /2)x - 4