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 identify the slope from a point-slope equation?

Back

In the point-slope form y - y1 = m(x - x1), the slope m is the coefficient of (x - x1).

Front

What does the point (4, -7) represent in the equation y + 7 = -1/4(x - 4)?

Back

The point (4, -7) is a specific point on the line represented by the equation, where x = 4 and y = -7.

Front

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

Back

A slope of -3 indicates that for every 1 unit increase in x, the value of y decreases by 3 units, meaning the line descends from left to right.

Front

Convert the point-slope equation y - 5 = -3(x - 10) to slope-intercept form.

Back

To convert to slope-intercept form, distribute and simplify: y = -3x + 35.

Front

What is the significance of the point (10, 5) in the equation y - 5 = -3(x - 10)?

Back

The point (10, 5) is a point on the line described by the equation, confirming that the line passes through this coordinate.

Front

How do you find the y-intercept from a point-slope equation?

Back

To find the y-intercept, convert the point-slope form to slope-intercept form (y = mx + b) and identify the value of b.

Front

What is the slope of the line represented by the equation y + 1 = -3(x - 5)?

Back

The slope of the line is -3, as indicated by the coefficient of (x - 5) in the equation.

Front

Write the point-slope form of the line with slope 2 that passes through the point (-4, 3).

Back

The point-slope form is y - 3 = 2(x + 4).

Front

What is the first step to write an equation in point-slope form?

Back

Identify a point (x1, y1) on the line and the slope m.