Writing equations from two points

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 (m) between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the y-intercept represent in a linear equation?

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

Given points (x1, y1) and (x2, y2), how do you write the equation of the line?

Back

First, calculate the slope m. Then use the point-slope form: y - y1 = m(x - x1) and rearrange to slope-intercept form.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

How can you determine if two points lie on the same line?

Back

Calculate the slope between the two points; if the slopes are equal, the points lie on the same line.

Front

What is the equation of the line that passes through (0, 0) and (1, 2)?

Back

The equation is y = 2x.

Front

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

Back

Start with y - y1 = m(x - x1) and solve for y to get y = mx + (y1 - mx1).

Front

What is the formula for the y-intercept when given the slope and a point?

Back

If you have the slope m and a point (x1, y1), the y-intercept b can be found using b = y1 - mx1.

Front

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

Back

The equation is y = 2x - 1.