write an equation in standard form of a line with a slope of 3 and a negative y- intercept
The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the slope is 3 and the y-intercept is negative, we can write the equation as:
y = 3x - b,
where b is a positive number.
To convert this equation into standard form, Ax + By = C, we move all the terms to one side of the equation:
-3x + y = b.
To make the y-intercept negative, let's replace b with -b:
-3x + y = -b.
Since b is a positive number, let's multiply the whole equation by -1 to make the coefficient of x positive:
3x - y = b.
Therefore, the equation in standard form of a line with a slope of 3 and a negative y-intercept is 3x - y = b.
To write the equation of a line in standard form with a slope of 3 and a negative y-intercept, we can use the formula: y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the slope (m) is 3 and the y-intercept (b) is negative, we can substitute these values into the equation.
The equation of the line becomes: y = 3x - b
Since b is negative, let's rewrite it as -c to represent a positive value: y = 3x + (-c)
Now, in standard form, the equation should be written with all the variables and constants on one side, so let's rearrange the equation: -3x + y = -c
To make the equation in standard form, we want to have the coefficients of x and y as integers, and the constant term (c) positive. Therefore, we can multiply the equation by -1 to make all the coefficients positive: 3x - y = c
Hence, the equation in standard form with a slope of 3 and a negative y-intercept is 3x - y = c, where c is a positive constant.