Determining Points on Linear Equations

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 it mean for a point to lie on a line represented by a linear equation?

Back

A point (x, y) lies on a line if, when the x-coordinate is substituted into the linear equation, the resulting y-value matches the y-coordinate of the point.

Front

How do you determine if the point (2, 3) lies on the line y = 2x + 1?

Back

Substitute x = 2 into the equation: y = 2(2) + 1 = 5. Since 5 does not equal 3, the point (2, 3) does not lie on the line.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.

Front

What is the slope of the line y = -x + 2?

Back

The slope is -1, as it is the coefficient of x in the equation.

Front

How do you check if the point (1, 0) lies on the line y = -x + 2?

Back

Substitute x = 1 into the equation: y = -1 + 2 = 1. Since 1 does not equal 0, the point (1, 0) does not lie on the line.

Front

What is the y-intercept of the line y = 2x - 9?

Back

The y-intercept is -9, as it is the constant term in the equation.

Front

How do you determine if the point (4, -1) lies on the line y = 2x - 9?

Back

Substitute x = 4 into the equation: y = 2(4) - 9 = 8 - 9 = -1. Since -1 equals -1, the point (4, -1) lies on the line.

Front

What does the term 'slope' refer to in a linear equation?

Back

The slope refers to the steepness of the line, calculated as the rise over run (change in y over change in x).

Front

How do you find the slope of the line given by the equation y = -2x + 3?

Back

The slope is -2, as it is the coefficient of x in the equation.