Answer:
Standard form: 3x + 4y = -40
Explanation:
General equation of the standard form:
The general equation of the standard form of a line is given by:
Ax + By = C. where:
- A, B, and C are constants.
Identifying the form of y = -3/4x - 10:
y = -3/4x - 10 is in the slope-intercept form of a line, whose general equation is given by:
y = mx + b, where:
- m is the slope,
- and b is the y-intercept.
Converting from slope-intercept form to standard form:
Thus, we can convert from slope-intercept form to standard form by isolating -10 on the right-hand side.
First, let's clear the fraction by multiplying the entire equation by 4:
4(y = -3/4x - 10)
4y = -12/4x - 40
4y = -3x - 40
Now, we can add 3x to both sides to have the equation in standard form:
(4y = -3x - 40) + 3x
3x + 4y = -40
Therefore, 3x + 4y = -40 is standard form of the line, given the equation y = -3/4x - 10.