Slope Intercept Form

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

What does the slope (m) represent in the slope-intercept form?

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 the slope-intercept form?

Back

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

Front

If the slope of a line is -2, what does this indicate about the line's direction?

Back

A slope of -2 indicates that for every 1 unit increase in x, y decreases by 2 units, meaning the line descends.

Front

Write the equation of a line with a slope of 3 and a y-intercept of 4.

Back

The equation is y = 3x + 4.

Front

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

Back

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

Front

What is the slope of the line represented by the equation y = -4x + 5?

Back

The slope is -4.

Front

Interpret the slope of the line y = 1/2x + 3 in a real-world context.

Back

The slope of 1/2 means that for every hour (x), the temperature (y) increases by 0.5 degrees.

Front

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

Back

Using point-slope form, the equation is y - 3 = -1(x - 2), which simplifies to y = -x + 5.

Front

If a line has a slope of 0, what does this indicate about the line?

Back

A slope of 0 indicates a horizontal line, meaning y remains constant regardless of x.