5.4 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: y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

How do you convert a point-slope equation to slope-intercept form?

Back

To convert from point-slope form (y - y_1 = m(x - x_1)) to slope-intercept form (y = mx + b), solve for y.

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, indicating 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 for every 1 unit increase in x, y decreases by 3 units, meaning the line descends from left to right.

Front

Back

The slope of the line is -\frac{5}{4}.

Front

How do you find a point on a line given in point-slope form?

Back

To find a point on a line given in point-slope form, substitute any value for x into the equation and solve for y.

Front

Back

The point (4, 4) is a specific point through which the line passes, confirming that the equation is valid.

Front

What is the equation of a line with slope 1/3 that passes through the point (4, 4)?

Back

Front

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

Back

To determine if a point (x, y) lies on a line, substitute the x-value into the equation and check if the resulting y-value matches.

Front

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

Back