Unit 8.3 Lesson 10: Solutions to Linear Equations Practice

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you find the value of y in the equation 3x + y = 5 when x = 1?

Back

Substituting x = 1 into the equation gives 3(1) + y = 5, which simplifies to y = 2.

Front

What does it mean for a point to be a solution to a linear equation?

Back

A point is a solution to a linear equation if it satisfies the equation when the coordinates of the point are substituted into it.

Front

Which points are solutions to the equation 3x + y = 5?

Back

The point (2,1) is not a solution because 3(2) + 1 ≠ 5, while (0,4) is a solution because 3(0) + 4 = 4.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

What does it mean for points to be 'on' the line of a linear equation?

Back

Points that are 'on' the line of a linear equation are solutions to the equation, meaning they satisfy the equation when substituted.

Front

How can you determine if a point is on the line of a linear equation?

Back

To determine if a point is on the line, substitute the x and y values of the point into the equation. If the equation holds true, the point is on the line.

Front

What is the equation of a line with a slope of 4 and a y-intercept of 3?

Back

The equation is y = 4x + 3.