5.5 Point-Slope Form

Front

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

Back

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

Front

How do you find the slope (m) between 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 of a line represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that the line is decreasing; for every 1 unit increase in x, y decreases by 3 units.

Front

Convert the equation y + 1 = -3(x - 5) to slope-intercept form.

Back

The slope-intercept form is y = -3x + 14.

Front

What is the significance of the point (5, -1) in the equation y + 1 = -3(x - 5)?

Back

The point (5, -1) is a specific point on the line described by the equation.

Front

Write the point-slope form for the line that passes through (2, 4) with a slope of 2.

Back

y - 4 = 2(x - 2).

Front

How do you determine if a point lies on a line given in point-slope form?

Back

Substitute the x-value of the point into the equation and check if the resulting y-value matches the y-value of the point.

Front

What is the relationship between point-slope form and slope-intercept form?

Back

Point-slope form can be converted to slope-intercept form (y = mx + b) by solving for y.

Front

If a line is represented by y - 3 = 1(x + 2), what is the slope?

Back

The slope of the line is 1.