Answer
Equation of the line in slope-intercept form is
y = -3x - 7
Step-by-step explanation
Two lines that are parallel to each other have the same slopes.
So, we just need the slope of the line 9x + 3y = 8, and the point given for the line we need to write the equation of that line.
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
To find the slope of the line, we need to put the equation given in the form of y = mx + b
9x + 3y = 8
3y = -9x + 8
Divide through by 3
(3y/3) = (-9x/3) + (8/3)
y = -3x + (8/3)
Comparing this with y = mx + b, we can see that
m = slope = -3
So for our line,
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
m = slope = -3
Point = (x₁, y₁) = (-1, -4)
x₁ = -1
y₁ = -4
y - y₁ = m (x - x₁)
y - (-4) = -3 (x - (-1))
y + 4 = -3 (x + 1)
y + 4 = -3x - 3
y = -3x - 3 - 4
y = -3x - 7
Hope this Helps!!!