Question

A line goes through points (0, 2) and (1, 1). What is the x-coordinate of the intersection of this line with the line y=3x+3?

Answer 1

Answer:

The x-coordinate of the intersection both lines is $x=-\frac{1}{4}$

Step-by-step explanation:

step 1

Find the equation of the line that passes through points (0, 2) and (1, 1).

Find the slope

$m=(1-2)/(1-0)=-1$

The equation of the line in slope intercept form is

$y=mx+b$

we have

$m=-1$

$b=2$ ----> the y-intercept is given

substitute

$y=-x+2$ ---> equation A

step 2

Solve the system of equations

$y=-x+2$ ---> equation A

$y=3x+3$ ----> equation B

Solve the system by substitution

Equate equation A and equation B

$3x+3=-x+2$

solve for x

$3x+x=2-3\\4x=-1\\x=-\frac{1}{4}$

therefore

The x-coordinate of the intersection both lines is $x=-\frac{1}{4}$

Answer 2

The x-coordinate of the point of intersection of the two lines will be $-\dfrac{1}{4}$.

Given information:

A line goes through points (0, 2) and (1, 1).

The given line intersects the line $y=3x+3$.

Now, the equation of the given line using two-point slope form can be written as,

$y-2=\dfrac{1-2}{1-0}(x-0)\\y-2=-x\\y=-x+2$

Now, the point of intersection of two lines will be,

$y=3x+3\\y=-x+2\\0=4x+1\\x=-\dfrac{1}{4}\\y=\dfrac{9}{4}$

Therefore, the x-coordinate of the point of intersection of the two lines will be $-\dfrac{1}{4}$.

For more details, refer to the link:

https://brainly.com/question/20632687