Standard Form to Slope Intercept Form

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is 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 by isolating it on one side of the equation.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing the equation of a line as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

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

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

How can 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 is the graphical representation of the equation 5x + 2y = 10?

Back

To graph the equation 5x + 2y = 10, convert it to slope-intercept form and plot the y-intercept and use the slope to find another point.

Front

What is the first step in converting the equation 2x + 4y = 8 into slope-intercept form?

Back

The first step is to subtract 2x from both sides to isolate the term with y.

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 and the direction of the line; A affects the x-component and B affects the y-component.

Front

How do you identify the slope and y-intercept from the equation y = 3x + 4?

Back

In the equation y = 3x + 4, the slope (m) is 3 and the y-intercept (b) is 4.