What is an equation, in standard form, of a line through (-1,2) with the same slope as the line 3x+y=-2
The line 3x+y=-2 can be written in slope-intercept form as y = -3x - 2.
To find the equation of the line with the same slope passing through (-1,2), we can substitute these values into the slope-intercept form.
Using the point-slope form, y - y₁ = m(x - x₁), where (x₁, y₁) = (-1, 2) and m represents the slope.
Substituting the values into the equation, we have:
y - 2 = -3(x - (-1))
y - 2 = -3(x + 1)
y - 2 = -3x - 3
y = -3x - 1
Thus, an equation in standard form of the line through (-1,2) with the same slope as the line 3x+y=-2 is 3x + y = -1.
To find the equation of a line with the same slope as another line, we need to manipulate the given equation into the standard form (Ax + By = C) and then substitute the given point into the equation.
Let's start by rearranging the given equation in slope-intercept form (y = mx + b), where m represents the slope:
3x + y = -2.
y = -3x - 2.
So, the slope (m) of the given line is -3.
Now, let's use the point-slope form of a line (y - y1 = m(x - x1)) to find the equation of the line passing through (-1, 2) with a slope of -3:
y - 2 = -3(x - (-1)).
y - 2 = -3(x + 1).
y - 2 = -3x - 3.
Now, let's rearrange this equation into standard form to get the final answer:
3x + y = -3 + 2.
3x + y = -1.
Thus, the equation in standard form of the line passing through (-1, 2) with the same slope as the line 3x + y = -2 is 3x + y = -1.
To find the equation of a line in standard form with the same slope as the line 3x + y = -2 and passing through the point (-1, 2), we need to follow these steps:
Step 1: Convert the given equation into slope-intercept form (y = mx + b), where m represents the slope:
3x + y = -2
Subtract 3x from both sides:
y = -3x - 2
Step 2: Determine the slope of the given line. In this case, the slope is -3.
Step 3: Since we want to find a line with the same slope, we can use the point-slope form of a line:
y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Step 4: Substitute the values of the given point (-1, 2) and the slope (-3) into the equation from step 3:
y - 2 = -3(x - (-1))
Step 5: Simplify the equation:
y - 2 = -3(x + 1)
Step 6: Distribute -3 to the terms inside the parentheses:
y - 2 = -3x - 3
Step 7: Move the constant term to the other side:
y = -3x - 3 + 2
Step 8: Simplify the equation further:
y = -3x - 1
Finally, the equation of the line in standard form with the same slope as the line 3x + y = -2 and passing through the point (-1, 2) is given by y = -3x - 1.