Question

Select the correct inequality for the graph below: A solid line passing through points (1, 2) and (2, 5) has shading below. y < 3x − 1 y ≤ 3x − 1 y ≥ 3x − 1 y > 3x − 1

Answer 1

Here is your answer:

Solving the equation:

• $(5-2)\div(2-1)= 3$
• $\frac{y - y1}{(x - x1) }$
• $y-5=3(x-2)$
• $y= 3x- 6+ 5$
• " $y= 3x-1$ " or option B.

Hope this helps!

Answer 2

Step 1

Find the equation of the line that passes through points $(1, 2)$ and $(2, 5)$

Find the slope of the line

The formula to calculate the slope is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{5-2}{2-1}$

$m=\frac{3}{1}$

$m=3$

Find the equation of the line

The equation of the line into slope-point form is equal to

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

we have

$m=3$

$(1, 2)$

substitutes

$y-2=3(x-1)$

$y=3x-3+2$

$y=3x-1$

Step 2

Find the equation of the inequality

we know that

The solution is the shaded area below the solid line

therefore

the inequality is

$y\leq 3x-1$

the answer is

$y\leq 3x-1$

see the attached figure to better understand the problem