Writing Equations of Lines Given a Point and a Slope

Front

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

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you find the equation of a line given a point and a slope?

Back

To find the equation of a line given a point (x₀, y₀) and a slope m, use the point-slope form: y - y₀ = m(x - x₀). You can then rearrange it to slope-intercept form.

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 and the direction it goes (positive slope means the line rises, negative slope means it falls).

Tags

CCSS.8.EE.B.5

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert from point-slope form (y - y₀ = m(x - x₀)) to slope-intercept form (y = mx + b), solve for y to isolate it on one side.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the formula for calculating the slope between two points (x₁, y₁) and (x₂, y₂)?

Back

The slope (m) between two points is calculated using the formula m = (y₂ - y₁) / (x₂ - x₁).

Tags

CCSS.8.EE.B.5

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in y regardless of the change in x.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x is 0, leading to division by zero.

Tags

CCSS.8.EE.B.5

Front

How do you determine the equation of a line given a slope of 1 and a point (-5, -7)?

Back

Using the point-slope form: y - (-7) = 1(x - (-5)), which simplifies to y = x - 2.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.

Tags

CCSS.8.EE.B.5