Point Slope from Graphs

Front

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

Back

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

Front

How do you identify the slope from a graph?

Back

The slope (m) is calculated as the rise over run, which is the change in y divided by the change in x between two points on the line.

Front

What does the term 'rise' refer to in the context of slope?

Back

'Rise' refers to the vertical change between two points on a line.

Front

What does the term 'run' refer to in the context of slope?

Back

'Run' refers to the horizontal change between two points on a line.

Front

How can you write the point-slope equation using a point on the line?

Back

To write the point-slope equation, substitute the coordinates of the point (x₁, y₁) and the slope m into the formula: y - y₁ = m(x - x₁).

Front

If a line has a slope of 2 and passes through the point (3, 4), what is the point-slope equation?

Back

The point-slope equation is: y - 4 = 2(x - 3).

Front

What is the significance of the point-slope form in graphing?

Back

The point-slope form allows you to easily graph a line by starting from a known point and using the slope to find other points.

Front

Can the point-slope form be converted to slope-intercept form?

Back

Yes, by rearranging the point-slope equation to solve for y, you can convert it to slope-intercept form (y = mx + b).

Front

What is an example of a point-slope equation with a negative slope?

Back

An example is: y + 2 = -3(x - 1), where the slope is -3.

Front

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

Back

Substitute the x-coordinate of the point into the line's equation and see if the resulting y-value matches the y-coordinate of the point.