Question

On a coordinate plane, a line goes through (0, negative 4) and (12, 6). A point is at (12, negative 2). What is the equation of the line that is parallel to the given line and passes through the point (12, −2)? y = –Six-fifths x + 10 y = –Six-fifths x + 12 y = –Five-sixths x – 10 y = Five-sixths x – 12

Answer 1

Answer:

y = Five-sixths x – 12

Step-by-step explanation:

Given that the line goes through points (0,-4) and (12,6) then the slope of the line can be calculated as;

m=rise/run

m=6--4/12-0  = 10/12 = 5/6

A line that is parallel to this line will have a slope of 5/6.

If it passes through point (12,-2) then the equation will be;

Points (12,-2) , (x,y) , m=5/6

y--2/x-12 = 5/6

y+2/x-12 =5/6---------------------perform cross multiplication

6(y+2) = 5(x-12)

6y+12=5x-60--------------collect like terms

6y=5x-60-12

6y=5x-72

y= 5/6x -12

Answer 2

Answer:

$f(x)=\frac{5}{6}x-12$

Step-by-step explanation:

1) So let's first calculate the equation of the line that goes through (0,-4) and (12,6).

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\Rightarrow m=\frac{6-(-4)}{12-0}\Rightarrow m=\frac{10}{12}\Rightarrow m=\frac{5}{6}\\\Rightarrow f(x)=\frac{5}{6}x+b\Rightarrow 6=\frac{5}{6}*(12)+b\Rightarrow 6=10+b\Rightarrow b=-4\\f(x)=\frac{5}{6}x-4$

2) As the second line is parallel, they share the same slope value.

so $m_{1}=m_{2}=\frac{5}{6}$

Plugging it in x-coordinate a y-coordinate (12,-2)

$f(x)=\frac{5}{6}x+b\Rightarrow -2=(12)\frac{5}{6}+b\Rightarrow -2=10+b\Rightarrow b=-12\therefore f(x)=\frac{5}{6}x-12$

(Check the graph)