What is an equation, in standard form, of a line through (−1, 2) with the same slope as the line 3x+y=-2
To find the equation of a line with the same slope as the line 3x + y = -2, we need to first write the given equation in slope-intercept form (y = mx + b), where m is the slope.
Rearranging the equation 3x + y = -2 to isolate y, we get y = -3x - 2. Hence, the slope of this line is -3.
Now, using the slope-intercept form (y = mx + b), we have:
y = -3x + b.
We know that the line passes through the point (-1, 2), so we can substitute these coordinates into the equation:
2 = -3(-1) + b.
Simplifying this equation, we have:
2 = 3 + b.
Now, solve for b:
b = 2 - 3 = -1.
Therefore, the equation of the line with the same slope as 3x + y = -2, passing through the point (-1, 2), is:
y = -3x - 1.
To find the equation of a line with the same slope as the line 3x + y = -2, we first need to rewrite the given equation in slope-intercept form, y = mx + b, where m represents the slope.
Starting with 3x + y = -2:
1. Subtract 3x from both sides of the equation to isolate the y-term:
y = -3x - 2
Now we can determine the slope of the line. The slope-intercept form of an equation is y = mx + b, where m represents the slope.
In this case, the slope (m) is -3.
Now that we know the slope (-3) and have a point on the line (-1, 2), we can use the point-slope form of a linear equation to determine the equation of the line.
The point-slope form is:
y - y1 = m(x - x1),
where (x1, y1) represents the coordinates of a point on the line.
Using the point (-1, 2) and the slope (-3) in the point-slope form, we get:
y - 2 = -3(x - (-1))
y - 2 = -3(x + 1)
Expanding the equation:
y - 2 = -3x - 3
Finally, moving the terms around to obtain the standard form, let's add 3x to both sides:
3x + y - 2 = -3
The equation, in standard form, of a line passing through (-1, 2) with the same slope as the line 3x + y = -2 is:
3x + y - 2 = -3.
To find the equation of a line with the same slope as the line 3x + y = -2 passing through the point (-1, 2), we will follow a few steps:
Step 1: Determine the slope of the given line.
The given line is written in standard form, Ax + By = C, where A, B, and C are coefficients. To find the slope, we need to rewrite the equation in slope-intercept form, y = mx + b, where m represents the slope.
Rewrite the given equation 3x + y = -2:
y = -3x - 2 (subtract 3x from both sides)
The slope of this line is -3.
Step 2: Use the slope and the given point to write the equation.
We have the slope (-3) and the point (-1, 2).
The point-slope form of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.
Substituting the values, we get:
y - 2 = -3(x - (-1)) (substitute -1 for x1 and 2 for y1, and -3 for m)
Simplifying:
y - 2 = -3(x + 1) (simplify -3(x - (-1)) to -3(x + 1))
Expand the equation:
y - 2 = -3x - 3 (distribute -3 to x and 1)
Now, let's rearrange this equation into standard form, Ax + By = C. To do so, move all the variables to the left side and constants to the right side:
3x + y = -1
So, the equation in standard form of a line through (-1, 2) with the same slope as the line 3x + y = -2 is 3x + y = -1.