Question

(1 point)
find an equation for of each of the lines in the figure.
line a (in red) has equation y=
line b (in blue) has equation y=

Explanation:

Step1: Find slope of line A

Let two points on line A be $(0,1)$ and $(2,3)$. The slope $m_A=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 1}{2-0}=1$.

Step2: Find y - intercept of line A

The line A intersects the y - axis at $(0,1)$, so the y - intercept $b_A = 1$.

Step3: Write equation of line A

Using the slope - intercept form $y=mx + b$, the equation of line A is $y = 1x+1=x + 1$.

Step4: Find slope of line B

Let two points on line B be $(0,6)$ and $(2,4)$. The slope $m_B=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 6}{2-0}=-1$.

Step5: Find y - intercept of line B

The line B intersects the y - axis at $(0,6)$, so the y - intercept $b_B = 6$.

Step6: Write equation of line B

Using the slope - intercept form $y=mx + b$, the equation of line B is $y=-1x + 6=-x + 6$.

Answer:

Line A: $y=x + 1$
Line B: $y=-x + 6$