Writing Equations from a Graph

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 identify the slope from a graph?

Back

The slope is the ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

If a line has a slope of 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit increase in x, the value of y increases by 2 units, making the line steep.

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0, indicating no change in y as x changes.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined, as it would involve division by zero (change in x is 0).

Front

How can you find the equation of a line given its slope and a point on the line?

Back

You can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

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

Back

Using point-slope form: y - 2 = -3(x - 1) simplifies to y = -3x + 5.

Front

How do you convert the equation y = 2x + 4 to standard form?

Back

To convert to standard form, rearrange to 2x - y = -4.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates.