Point Slope Form & Systems of Equations using Graphing

Front

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

Back

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

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

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

Back

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

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of x and y that satisfy both equations.

Front

What does it mean if a system of equations has no solution?

Back

The lines are parallel and do not intersect, indicating that there are no values of x and y that satisfy both equations.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines coincide, meaning they are the same line and every point on the line is a solution.

Front

How do you graph a line using point-slope form?

Back

Start at the point (x₁, y₁) and use the slope m to find another point by rising and running.

Front

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

Back

-3, as it is the coefficient of (x - 5) in the point-slope form.

Front

How can you convert point-slope form to slope-intercept form?

Back

Distribute and rearrange the equation to isolate y on one side.

Front

What is the y-intercept of the line y - 6 = -2(x + 5)?

Back

-4, found by rearranging to slope-intercept form.