The linear equation 16x - 4y = 2 represents a straight line in a Cartesian plane, defined by its slope and y-intercept.
The linear equation 16x - 4y = 2 can be analyzed in terms of its form, slope, and y-intercept.
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.
In this equation, the coefficients are 16, -4, and 2 for x, y, and the constant term, respectively.
To find the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can rearrange the given equation:
16x - 4y = 2
-4y = -16x + 2
y = 4x - 0.5
Now, we can interpret the equation. The coefficient of x, 4, represents the slope of the line. In this case, the slope is positive, indicating that as x increases, y also increases.
The constant term, -0.5, is the y-intercept, which is the point where the line crosses the y-axis.
So, the linear equation 16x - 4y = 2 describes a line with a slope of 4 and a y-intercept of -0.5.
This means that for every unit increase in x, y increases by 4, and the line intersects the y-axis at the point (0, -0.5).
The form and properties of linear equations is fundamental in algebra and graphing, providing insights into relationships between variables and helping in the visualization of mathematical concepts.