Unit 5: Linear Equations Flashcard

Front

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

Back

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

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept of a line?

Back

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

Front

What is the equation of a line with a slope of 2 that passes through the point (1, 3)?

Back

The equation is y = 2x + 1.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

How do you convert the point-slope form of a line to slope-intercept form?

Back

Start with y - y1 = m(x - x1) and solve for y to get y = mx + (y1 - mx1).

Front

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

Back

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

Front

Given the equation y = -3x + 4, what is the slope and y-intercept?

Back

The slope (m) is -3 and the y-intercept (b) is 4.