Writing Linear Equations Given a Point and Slope

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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 and the direction it goes (positive slope goes up, negative slope goes down).

Tags

CCSS.8.EE.B.5

Front

How do you find the y-intercept (b) of a linear equation?

Back

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

Front

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

Back

The slope-intercept form of a linear equation is 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 write the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Front

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

Back

The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

If a line has a slope of -2 and passes through the point (-1, 3), what is the equation of the line?

Back

Using point-slope form: y - 3 = -2(x + 1) simplifies to y = -2x + 1.

Front

What is the y-intercept of the line with the equation y = 3x + 4?

Back

The y-intercept is 4, which is the value of y when x = 0.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of the line that has a slope of 1/2 and passes through the point (2, 0)?

Back

Using the point-slope form: y - 0 = 1/2(x - 2) simplifies to y = 1/2x - 1, so the y-intercept is -1.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3