Find the equation of the line passing through (-1 , -4) and parallel to -7x+6y=8 slope intercept
Since your new line is parallel to the given line, it will differ only in the constant, so it will be
-7x + 6y = c
plug in the given point:
-7(-1) + 6(-4) = c
c = -17
new equation:
-7x + 6y = -17
or
6y = 7x - 17
y = (7/6)x - 17/6
To find the equation of a line parallel to a given line, we need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept.
The given equation is -7x + 6y = 8. Let's rearrange it to the slope-intercept form:
6y = 7x + 8
Divide both sides by 6:
y = (7/6)x + 4/3
The slope of this line is 7/6.
Since the line we are looking for is parallel to this line, it will have the same slope. Now, let's use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Using the given point (-1, -4), we have:
y - (-4) = (7/6)(x - (-1))
y + 4 = (7/6)(x + 1)
To convert this equation to the slope-intercept form, let's simplify it:
y + 4 = (7/6)x + 7/6
y = (7/6)x + 7/6 - 4
y = (7/6)x + 7/6 - 24/6
y = (7/6)x - 17/6
Therefore, the equation of the line passing through (-1, -4) and parallel to -7x + 6y = 8 is y = (7/6)x - 17/6.
To find the equation of a line parallel to the line -7x + 6y = 8, we need to determine the slope of the given line first.
The equation of the line -7x + 6y = 8 is in standard form. We can convert it into slope-intercept form (y = mx + b) to easily identify the slope.
Step 1: Rewrite the equation in slope-intercept form:
-7x + 6y = 8 (Add 7x to both sides to isolate y)
6y = 7x + 8 (Divide by 6 to isolate y)
y = (7/6)x + 8/6 (Simplify)
From the slope-intercept form, we can see that the slope of the given line is 7/6.
Since the desired line is parallel to the given line, it will have the same slope. Let's proceed to find the equation of the line that passes through the given point (-1, -4) with a slope of 7/6.
Step 2: Use the point-slope form of a line:
y - y₁ = m(x - x₁)
Substitute the values of the slope (m = 7/6) and the point (-1, -4) into the point-slope form:
y - (-4) = (7/6)(x - (-1))
y + 4 = (7/6)(x + 1)
Now, let's simplify the equation to slope-intercept form:
y + 4 = (7/6)x + (7/6)
y = (7/6)x + (7/6) - (24/6)
y = (7/6)x - (17/6)
Therefore, the equation of the line passing through (-1, -4) and parallel to -7x + 6y = 8 is y = (7/6)x - (17/6).