Write the equation of a line whose slope is the same as the line 3y=-2x+6 and passes through the point (-1,4)
3y=-2x+6
y=-2/3 x +6
y=-2/3 x +b
4=(-2/3)(-1) +b
b=4-(2/3)=10/3
y=-2/3 x +10/3
To find the equation of a line with the same slope as the line 3y = -2x + 6, we need to rearrange the equation in the slope-intercept form, y = mx + b, where m represents the slope:
3y = -2x + 6
Divide both sides of the equation by 3:
y = (-2/3)x + 2
The slope of this line is -2/3.
To find the equation of a line that passes through the point (-1, 4) and has the same slope, we can use the point-slope form, y - y1 = m(x - x1):
y - 4 = -2/3(x - (-1))
Simplifying:
y - 4 = -2/3(x + 1)
Now, expand the equation:
y - 4 = (-2/3)x - 2/3
To isolate y, add 4 to both sides:
y = (-2/3)x - 2/3 + 4
Simplifying:
y = (-2/3)x - 2/3 + 12/3
y = (-2/3)x + 10/3
Therefore, the equation of the line with the same slope as 3y = -2x + 6 and passes through the point (-1, 4) is y = (-2/3)x + 10/3.
To find the equation of a line with a given slope and a point, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
Where:
m is the slope of the line
x is the x-coordinate of a point on the line
y is the y-coordinate of a point on the line
b is the y-intercept
In this case, we are given the equation of a line, 3y = -2x + 6, and we need to find the equation of another line with the same slope that passes through the point (-1, 4).
First, let's determine the slope of the given line. The equation is already in slope-intercept form, so we can directly read the slope from the equation. The slope, in this case, is -2/3.
Now, let's use the point-slope form of a linear equation to find the equation of the line passing through the point (-1, 4) with a slope of -2/3. The point-slope form is:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of the given point, and m is the slope.
Plugging in the values, we get:
y - 4 = -2/3(x - (-1))
Simplifying further:
y - 4 = -2/3(x + 1)
Distributing -2/3:
y - 4 = -2/3x - 2/3
Finally, rearrange the equation to get it in slope-intercept form:
y = -2/3x - 2/3 + 4
Simplifying:
y = -2/3x + 10/3
Therefore, the equation of the line with the same slope as 3y = -2x + 6 and passing through the point (-1, 4) is y = -2/3x + 10/3.