Linear Functions - Math

Use substution to solve this problem:

becomes and then is substituted into the second equation. Then solve for :

, so and to give the solution .

To solve for the -intercept, set to zero and solve for :

To solve for the -intercept, set to zero and solve for :

Slope-intercept form is .

A vertical line has infinitely many values of but only one value of . Thus, vertical lines are of the form , where is a real number. The only equation of this form is .

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form , where is a constant. Horizontal lines have a slope of . The only equation of this form is .

A vertical line is one in which the values can vary. Namely, there is only one possible value for , and can be any number. Thus, by this description, the only vertical line listed is .

A line with a slope of zero will be horizontal. A horizontal line has only one possible value for , and can be any value.

Thus, the only given equation which fits this description is .

Use substution to solve this problem:

becomes and then is substituted into the second equation. Then solve for :

, so and to give the solution .

To solve for the -intercept, set to zero and solve for :

To solve for the -intercept, set to zero and solve for :

Slope-intercept form is .

A vertical line has infinitely many values of but only one value of . Thus, vertical lines are of the form , where is a real number. The only equation of this form is .

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form , where is a constant. Horizontal lines have a slope of . The only equation of this form is .

A vertical line is one in which the values can vary. Namely, there is only one possible value for , and can be any number. Thus, by this description, the only vertical line listed is .

A line with a slope of zero will be horizontal. A horizontal line has only one possible value for , and can be any value.

Thus, the only given equation which fits this description is .

Use substution to solve this problem:

becomes and then is substituted into the second equation. Then solve for :

, so and to give the solution .

To solve for the -intercept, set to zero and solve for :

To solve for the -intercept, set to zero and solve for :

Slope-intercept form is .

A vertical line has infinitely many values of but only one value of . Thus, vertical lines are of the form , where is a real number. The only equation of this form is .

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form , where is a constant. Horizontal lines have a slope of . The only equation of this form is .

A vertical line is one in which the values can vary. Namely, there is only one possible value for , and can be any number. Thus, by this description, the only vertical line listed is .