Point-Slope and Standard Form Flashcard Review

Front

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

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert an 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 of the equation.

Front

What is point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by the formula y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) between two points is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the zero of a function?

Back

The zero of a function is the value of x that makes the function equal to zero (f(x) = 0).

Front

How do you determine if a point lies on a line given by an equation?

Back

To determine if a point (x, y) lies on a line given by an equation, substitute the x-value into the equation and check if the resulting y-value matches the y-value of the point.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x; it indicates how steep the line is and the direction it goes (positive or negative).

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, represented by the value of y when x = 0.

Front

How can you write the equation of a line given a point and a slope?

Back

You can write the equation of a line using the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

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 of the line can be found using the formula m = -A/B.