Question

2. Write the equation of the line parallel to y = -4x/3 + 5 thru (-6,1). Show all work.​

Answer 1

Answer:

$\boxed {\boxed {\sf y= - \frac{4}{3} x -7}}$

Step-by-step explanation:

We can find the equation using the point-slope formula.

$y-y_1=m(x-x_1)$

where (x₁, y₁) is the point and m is the slope.

We already know the point is (-6,1). We must find the slope.

We are told the line is parallel to y=-4x/3 +5. Since this line is in y=mx+b form, the slope (m) must be -4/3. Parallel lines have equal slopes, so the line we are finding also has a slope of -4/3

Next, define values for the variables.

$x_1= -6 \\y_1= 1\\m= - \frac{4}{3}$

Substitute the values into the formula.

$y-1= - \frac{4}{3} (x--6)$

$y-1= - \frac{4}{3} (x+6)$

Now put the equation into the form y=mx+b. First, distribute the -4/3 .

$y-1= - \frac{4}{3} *x+ - \frac {4}{3}*6$

$y-1= - \frac{4}{3} x - 8$

Add 1 to both sides to isolate y.

$y-1+1= - \frac{4}{3} x - 8+1$

$y= - \frac{4}{3} x -7$

The equation of the line is y=-4/3x -7