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 3x+y=-2 and passing through the point (-1,2), we need to determine the slope of the given line and then use the point-slope form of a line.
The given line is 3x+y=-2, which can be rewritten in slope-intercept form as y = -3x - 2.
Comparing the equation with the standard slope-intercept form y = mx + b, we see that the slope m of the given line is -3.
Now, let's use the point-slope form of a line, which is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Substituting the values (-1, 2) and m = -3 into the point-slope form, we get:
y - 2 = -3(x - (-1))
Simplifying the equation:
y - 2 = -3(x + 1)
y - 2 = -3x - 3
3x + y = -1
Therefore, the equation in standard form of the line passing through the point (-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 the line 3x + y = -2 and passing through the point (-1, 2), we can follow these steps:
Step 1: Convert the given equation 3x + y = -2 to slope-intercept form (y = mx + b), where m represents the slope.
Start by isolating y on one side of the equation.
Subtract 3x from both sides.
y = -3x - 2
Step 2: The equation y = -3x - 2 is in slope-intercept form (y = mx + b), where m represents the slope, which is -3 in this case.
Step 3: Use the slope (-3) and the given point (-1, 2) to find the equation of the line.
Plug in the values of x and y for the point (-1, 2) and the slope (-3) into the point-slope form (y - y1 = m(x - x1)).
y - 2 = -3(x - (-1))
Simplify the right side of the equation.
y - 2 = -3(x + 1)
Apply the distributive property.
y - 2 = -3x - 3
Add 2 to both sides to isolate y.
y = -3x - 3 + 2
y = -3x - 1
Therefore, the equation of the line through (-1, 2) with the same slope as the line 3x + y = -2 is y = -3x - 1 in standard form.
To find an equation of a line with the same slope, we need to determine the slope of the given line 3x + y = -2.
First, let's rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept:
3x + y = -2
y = -3x - 2
From the slope-intercept form, we can determine that the slope of the given line is -3.
Now, we can use the point-slope form of a linear equation to find the equation of the line passing through (-1, 2) with a slope of -3:
y - y1 = m(x - x1)
Plugging in the values (x1 = -1, y1 = 2, and m = -3), we can write the equation as:
y - 2 = -3(x - (-1))
Simplifying further:
y - 2 = -3(x + 1)
y - 2 = -3x - 3
y = -3x - 1
Therefore, the equation, in standard form, of a line passing through (-1, 2) with the same slope as the line 3x + y = -2 is: y = -3x - 1.