(MCA) 4.4 (Flashcard) Writing linear Equations in Standard form.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

Convert the equation 3x = 7y - 5 into standard form.

Back

3x - 7y = -5.

Front

How do you graph a linear equation in standard form?

Back

To graph a linear equation in standard form, find the x-intercept (set y=0) and the y-intercept (set x=0), then plot these points and draw a line through them.

Front

What does the slope-intercept form of a linear equation look like?

Back

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

Front

How can you convert from slope-intercept form to standard form?

Back

Rearrange the equation y = mx + b to the form Ax + By = C by moving all terms involving x and y to one side.

Front

What is the significance of the coefficients A and B in the standard form of a linear equation?

Back

The coefficients A and B determine the slope of the line and its orientation in the coordinate plane.

Front

Given the equation 2x + 3y = 3, what are the x and y intercepts?

Back

The x-intercept is (1.5, 0) and the y-intercept is (0, 1).

Front

Identify the equation that matches the graph of a line with a slope of 3 and y-intercept of -5.

Back

The equation is y = 3x - 5.

Front

What is the relationship between the standard form and the slope of a line?

Back

The slope can be found from the standard form Ax + By = C using the formula -A/B.

Front

Convert the equation 3x + 4y = 16 into slope-intercept form.

Back

The slope-intercept form is y = -rac{3}{4}x + 4.