Slope-Intercept form and Slope formula

Front

What is the slope formula?

Back

The slope formula is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where \( m \) is the slope, and \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.

Front

What does 'rise over run' mean in the context of slope?

Back

'Rise over run' refers to the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line, which defines the slope.

Front

How do you write an equation in slope-intercept form?

Back

The slope-intercept form of a linear equation is written as \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Front

What is the y-intercept in the equation \( y = 3x + 5 \)?

Back

The y-intercept is \( 5 \), which is the value of \( y \) when \( x = 0 \).

Front

If a line has a slope of 2, what does this indicate?

Back

A slope of 2 indicates that for every 1 unit increase in \( x \), \( y \) increases by 2 units.

Front

What is the slope of the line represented by the equation \( y = -4x + 1 \)?

Back

The slope of the line is \( -4 \).

Front

How do you find the slope from a graph?

Back

To find the slope from a graph, count the vertical change (rise) and the horizontal change (run) between two points on the line, then use the formula \( m = \frac{rise}{run} \).

Front

Write the slope-intercept form for a line with a slope of 1 and a y-intercept of -3.

Back

The equation is \( y = 1x - 3 \) or simply \( y = x - 3 \).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is \( 0 \) because there is no vertical change as you move along the line.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the run (horizontal change) is zero.