Standard Form and Linear Graphs

Front

What is Standard Form in linear equations?

Back

Standard Form is a way of writing linear equations in the form Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you convert a linear equation from Standard Form to Slope-Intercept Form?

Back

To convert from Standard Form (Ax + By = C) to Slope-Intercept Form (y = mx + b), solve for y to isolate it on one side.

Front

What does the slope of a line represent in a linear graph?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How can you determine if two lines are parallel using their equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the significance of the x-intercept in a linear graph?

Back

The x-intercept is the point where the line crosses the x-axis, represented as (a, 0) in the equation.

Front

How do you find the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does it mean for a linear equation to be in slope-intercept form?

Back

A linear equation is in slope-intercept form if it is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the relationship between the coefficients in Standard Form and the slope of the line?

Back

In Standard Form Ax + By = C, the slope can be found using the formula -A/B.

Front

How can you graph a linear equation given in Standard Form?

Back

To graph a linear equation in Standard Form, find the x-intercept and y-intercept, plot these points, and draw a line through them.