The line through (4,3),parallel to y=-4x+1
Write the equation in standard form
since the lines are parallel the slopes have to be the same -
by using the equation Y-Y1= m(X-X1)
where Y1= 3 ; X1= 4 and m= -4 (AKA slope of the original equation)
now plug in your values : Y-3 =-4(X-4)
and solve for Y
your answer should be - Y= -4X+19
*Always make sure your answer is correct by graphing!!*
Parallel lines have equal slopes:
m = -4, P1(4,3), P2(x,y).
m = (y-3)/(x-4) = -4.
y-3 = -4x + 16
Y = -4x + 19.
To find the equation of a line that is parallel to the given line, we need to use the fact that parallel lines have the same slope.
The given line has a slope of -4 because it is in the form y = mx + b, where m represents the slope. So, the line we are looking for will also have a slope of -4.
The general form of a linear equation is Ax + By = C. To write the equation in standard form, we need to rearrange it so that the coefficients of x, y, and the constant term are integers.
First, let's find the y-intercept (b) of the new line using the given point (4, 3). We will substitute this point into the equation and solve for b.
Using the point (4, 3) in the equation y = -4x + b:
3 = -4(4) + b
3 = -16 + b
b = 19
Now that we have the slope (-4) and the y-intercept (19), we can write the equation in slope-intercept form: y = -4x + 19.
To convert it to standard form, we need to eliminate the fraction by multiplying the entire equation by -1. The standard form requires that the coefficient of x be positive, so we will multiply through by -1.
Multiplying each term by -1 gives us:
-1y = 4x - 19
Finally, rearrange the terms in standard form to get:
4x + 1y = 19