Solving Slope-Intercept Systems

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

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

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

How do you determine the intersection point of two lines?

Back

To find the intersection point, solve the system of equations formed by the two lines simultaneously.

Front

Given the equations y = -1/5 x + 1 and y = 5 x - 77, find the intersection point.

Back

The intersection point is (15, -2).

Front

Convert the slope of -7 and y-intercept of -8 into slope-intercept form.

Back

The slope-intercept form is y = -7x - 8.

Front

Given the equations y = 1/4 x + 7 and y = -4 x - 27, find the intersection point.

Back

The intersection point is (-8, 5).

Front

What is the equation of a line with a slope of 4 and a y-intercept of 2?

Back

The equation is y = 4x + 2.

Front

How do you write the equation of a line that passes through two points?

Back

First, find the slope using the two points, then use the point-slope form to write the equation.