Question

determine the equation of the line for the given information: the graph has y-intercept (0, 6) and contains the point (2, 1). a. y = 2.5x + 6 b. y = -2.5x + 6 c. y = 6x + -2.5 d. y = 2x + 6 please select the best answer from the choices provided a b c d

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is $y = mx + b$, where $b$ is the y - intercept and $m$ is the slope. We know that the y - intercept $(0,6)$ means $b = 6$. So the equation of the line is of the form $y=mx + 6$.

Step2: Calculate the slope

We have two points: $(0,6)$ and $(2,1)$. The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 0,y_1 = 6,x_2=2,y_2 = 1$ into the formula, we get $m=\frac{1 - 6}{2-0}=\frac{- 5}{2}=- 2.5$.

Step3: Write the equation

Substituting $m=-2.5$ and $b = 6$ into the slope - intercept form $y=mx + b$, we get $y=-2.5x + 6$. We can also check by plugging the point $(2,1)$ into each option:

• Option a: $y = 2.5x+6$. When $x = 2$, $y=2.5\times2 + 6=5 + 6 = 11

eq1$.

• Option b: $y=-2.5x + 6$. When $x = 2$, $y=-2.5\times2+6=-5 + 6 = 1$, which matches.
• Option c: $y = 6x-2.5$. When $x = 2$, $y=6\times2-2.5 = 12 - 2.5=9.5

eq1$.

• Option d: $y = 2x+6$. When $x = 2$, $y=2\times2 + 6=4 + 6 = 10

eq1$.

Answer:

B. $y=-2.5x + 6$