Slope-Intercept Form and Point-Slope Form Review

A set of practice flashcards covering slope-intercept form, y-intercept, x-intercept, and the point-slope form with examples and methods for finding equations from given data.

What is the slope-intercept form of a line?

y = m x + b, where m is the slope and b is the y-intercept.

In the slope-intercept form y = mx + b, what does b represent?

The y-intercept: the point where the line crosses the y-axis (0, b).

How do you write the equation of a line when the slope m and y-intercept b are given?

y = m x + b.

How can you obtain the x-intercept from a line in slope-intercept form?

Set y = 0 and solve for x; the x-intercept is the x-coordinate where y = 0.

If the x-intercept is -4 and the y-intercept is 6, what are the intercept points?

x-intercept point: (-4, 0); y-intercept point: (0, 6).

How do you find the slope of a line from two points (x1, y1) and (x2, y2)?

m = (y2 - y1) / (x2 - x1).

What is the slope of the line through (-4, 0) and (0, 6)?

m = (6 - 0) / (0 - (-4)) = 6/4 = 3/2.

Given slope m = 3/2 and y-intercept b = 6, what is the equation in slope-intercept form?

y = (3/2)x + 6.

What is the point-slope form of a line through point (x1, y1) with slope m?

y - y1 = m (x - x1).

How would you write the equation of a line through the point (-1, -5) with slope -2 using point-slope form?

y - (-5) = -2 (x - (-1)) which simplifies to y = -2x - 7.

How do you convert a point-slope form equation y - y1 = m(x - x1) into slope-intercept form?

Expand and rearrange to y = mx + (y1 - m x1).

If given two points but no slope, what steps can you take to write the equation of the line?

Compute the slope from the two points, then use y = mx + b (find b using a known point) or use the point-slope form y - y1 = m(x - x1).

What is the x-intercept of a line?

The point where the line crosses the x-axis; y = 0, coordinates (x, 0).

What is the y-intercept of a line in slope-intercept form?

The coordinate where the line crosses the y-axis; x = 0, coordinates (0, b).