Is P(x, y) a Solution?

Drag the point to various positions (both ON and OFF the line). Pay attention to what you see here. Then, answer the questions that follow.

If a point [math]\left(x,y\right)[/math] LIES on a line with a given equation, what can we conclude?

[math]\left(x,y\right)[/math] is a solution to the equation. [math]\left(x,y\right)[/math] is not a solution to the equation.

If a point [math]\left(x,y\right)[/math] DOES NOT LIE on a line with a given equation, what can we conclude?

[math]\left(x,y\right)[/math] is a solution to the equation. [math]\left(x,y\right)[/math] is not a solution to the equation.

If we wanted to see whether [math]\left(4,-3\right)[/math] was a solution to the equation [math]3x-5y=27[/math], what would we need to do first?

Determine the truth value of the equation [math]3\left(4_{ }\right)-5\left(-3\right)=27[/math]. Substitute 4 for [i]y[/i] in the given equation Substitute -3 for [i]x[/i] in the given equation Determine the truth value of the equation [math]3\left(-3\right)-5\left(4\right)=27[/math]. Substitute 4 for [i]x[/i] in the given equation Substitute -3 for [i]y[/i] in the given equation

Is [math]\left(4,-3\right)[/math] a solution to the equation [math]3x-5y=27[/math]?

no yes

If we wanted to see whether [math]\left(-3,4\right)[/math] was a solution to the equation [math]3x-5y=-30[/math], what would we need to do first?

Substitute 4 for [i]x[/i] in the given equation Determine the truth value of the equation [math]3\left(4_{ }\right)-5\left(-3\right)=-30[/math]. Substitute -3 for [i]x[/i] in the given equation Substitute -3 for [i]y[/i] in the given equation Determine the truth value of the equation [math]3\left(-3\right)-5\left(4\right)=-30[/math]. Substitute 4 for [i]y[/i] in the given equation

Is [math]\left(-3,4\right)[/math] a solution to the equation [math]3x-5y=-30[/math]?

yes no

Is P(x, y) a Solution?

Drag the point to various positions (both ON and OFF the line). Pay attention to what you see here. Then, answer the questions that follow.

Information: Is P(x, y) a Solution?