Answer
The equation of the line is
y = -4x + 12
Step-by-step explanation
Two straight lines that are parallel to each other normally have the same slopes.
So, to write the equation for our required line, we need to extract the slope from the line that is parallel to it.
To do that, we will note that
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.
So, comparing this with y = -4x + 7
We can see that the slope of our required line is -4
To now write its equation, we will use the form of the equation of a straight line that uses the slope of the line and the coordinates of a point on the 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
For this line,
m = -4
(x₁, y₁) = (2, 4)
x₁ = 2
y₁ = 4
y - y₁ = m (x - x₁)
y - 4 = -4 (x - 2)
y - 4 = -4x + 8
y = -4x + 8 + 4
y = -4x + 12
Hope this Helps!!!