(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 identify the slope and y-intercept from the standard form of a linear equation?

Back

From the standard form Ax + By = C, the slope (m) can be found using m = -A/B, and the y-intercept (b) can be found using b = C/B.

Tags

CCSS.8.EE.B.5

Front

What does it mean for two lines to be parallel in terms of their equations?

Back

Two lines are parallel if they have the same slope, which means their equations will have the same coefficient for x when written in slope-intercept form.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the y-intercept in a linear equation?

Back

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

Front

Convert the equation 13 - 6x - y = 0 into standard form.

Back

6x + y = 13

Front

What is the relationship between the coefficients of x and y in a linear equation in standard form?

Back

The coefficients A and B in the standard form Ax + By = C determine the slope of the line and its orientation in the coordinate plane.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you determine if a point lies on the line represented by a linear equation?

Back

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

Front

What is the process for graphing a linear equation in standard form?

Back

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

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean for two lines to be perpendicular in terms of their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning one slope is the negative reciprocal of the other.

Tags

CCSS.8.EE.B.6