Question

Choose the system of equations which matches the following graph:

Answer 1

Answer:

Option a

- x + 2y = −10

3x − y = 12

Step-by-step explanation:

step 1

Find the equation of the line with negative slope

we know that

The line with negative slope has a y-intercept at (0,-5)  and passes through the point (2,-6)

Find the slope

$m=(-6+5)/(2-0)=-\frac{1}{2}$

The equation in slope intercept form is

$y=-\frac{1}{2}x-5$

Convert to standard form

Multiply by 2 both sides

$2y=-x-10\\x+2y=-10$

step 2

Find the equation of the line with positive slope

The line with positive slope has a x-intercept at (4,0)  and passes through the point (2,-6)

Find the slope

$m=(-6-0)/(2-4)=3$

The equation of the line in point slope form is equal to

$y-y1=m(x-x1)$

we have

$m=3\\point\ (4,0)$

substitute

$y-0=3(x-4)$

Convert to standard form

$y=3x-12\\3x-y=12$

therefore

The system of equations is

- x + 2y = −10

3x − y = 12