일차함수와 일차방정식

Find the $x$ and $y$ Intercepts from an Equation of a Line

In the following exercises, find the intercepts.

$y=5x$

Evaluate $3x+2$ when $x=-1$.

Solve $3x+2y=12$ for $y$ in general.

What is the difference between the equations of a vertical and a horizontal line?

Solve: $4x+3>23$.

Translate from algebra to English: $x<5$.

Evaluate $3x-2y$ when $x=1$, $y=-2$.

Determine whether each ordered pair is a solution to the inequality $y>x+4$:

ⓐ $(0,0)$ ⓑ $(1,6)$ ⓒ $(2,6)$ ⓓ $(-5,-15)$ ⓔ $(-8,12)$

Determine whether each ordered pair is a solution to the inequality $y>x-3$:

ⓐ $(0,0)$ ⓑ $(4,9)$ ⓒ $(-2,1)$ ⓓ $(-5,-3)$ ⓔ $(5,1)$

Determine whether each ordered pair is a solution to the inequality $y<x+1$:

ⓐ $(0,0)$ ⓑ $(8,6)$ ⓒ $(-2,-1)$ ⓓ $(3,4)$ ⓔ $(-1,-4)$

Determine whether each ordered pair is a solution to the inequality $y>x-1$:

• ⓐ $(0,1)$
• ⓑ $(-4,-1)$
• ⓒ $(4,2)$
• ⓓ $(3,0)$
• ⓔ $(-2,-3)$

Determine whether each ordered pair is a solution to the inequality $y>x-3$:

• ⓐ $(0,0)$
• ⓑ $(2,1)$
• ⓒ $(-1,-5)$
• ⓓ $(-6,-3)$
• ⓔ $(1,0)$

Determine whether each ordered pair is a solution to the inequality $y<x+2$:

• ⓐ $(0,3)$
• ⓑ $(-3,-2)$
• ⓒ $(-2,0)$
• ⓓ $(0,0)$
• ⓔ $(-1,4)$

Determine whether each ordered pair is a solution to the inequality $y<x+5$:

• ⓐ $(-3,0)$
• ⓑ $(1,6)$
• ⓒ $(-6,-2)$
• ⓓ $(0,1)$
• ⓔ $(5,-4)$

Determine whether each ordered pair is a solution to the inequality $x+y>4$:

• ⓐ $(5,1)$
• ⓑ $(-2,6)$
• ⓒ $(3,2)$
• ⓓ $(10,-5)$
• ⓔ $(0,0)$

Determine whether each ordered pair is a solution to the inequality $x+y>2$:

• ⓐ $(1,1)$
• ⓑ $(4,-3)$
• ⓒ $(0,0)$
• ⓓ $(-8,12)$
• ⓔ $(3,0)$

Explain why in some graphs of linear inequalities the boundary line is solid but in other graphs it is dashed.

For the equation $y=\frac{2}{3}x-4$

ⓐ is $(6,0)$ a solution? ⓑ is $(-3,-2)$ a solution?

Find the slope and y-intercept of the line $3x-y=12$.

Find the x- and y-intercepts of the line $2x-3y=12$.