Point-Slope Form w/ y=mx+b + Ax+By=C =) -30?s

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 convert from point-slope form to slope-intercept form?

Back

To convert from point-slope form (y - y₁ = m(x - x₁)) to slope-intercept form (y = mx + b), solve for y.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) 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 0, what does that indicate about the line?

Back

A slope of 0 indicates that the line is horizontal.

Front

What is the slope of a line that passes through the points (2, 3) and (4, 7)?

Back

The slope is m = (y₂ - y₁) / (x₂ - x₁) = (7 - 3) / (4 - 2) = 2.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x = 0; it is where the line crosses the y-axis.

Front

How do you find the slope from the equation Ax + By = C?

Back

Rearrange the equation to slope-intercept form (y = mx + b) to identify the slope m as -A/B.

Front

What is the significance of the point (x₁, y₁) in the point-slope form?

Back

The point (x₁, y₁) is a specific point on the line used to define the line's position.

Front

Write the point-slope form for a line with slope -3 passing through the point (2, 5).

Back

y - 5 = -3(x - 2).

Front

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

Back

Point-slope form can be converted to slope-intercept form, which is useful for graphing.