Standard Form

Standard Form is a way of writing numbers or equations in a specific format. For linear equations, it is typically written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

To find the slope, rearrange the equation into slope-intercept form (y = mx + b). The slope (m) is the coefficient of x. For 6x - y = 9, the slope is 6.

To find the y-intercept, set x = 0. For 2(0) - 5y = 35, solving gives y = -7. Thus, the y-intercept is (0, -7).

To find the x-intercept, set y = 0: x + 0 = -2, so x = -2. To find the y-intercept, set x = 0: 0 + y = -2, so y = -2. The intercepts are (-2, 0) and (0, -2).

To find the x-intercept, set y = 0: 5x = 15, so x = 3. To find the y-intercept, set x = 0: -3y = 15, so y = -5. The intercepts are (3, 0) and (0, -5).

For the x-intercept, set y = 0: 4x = 40, so x = 10. For the y-intercept, set x = 0: -5y = 40, so y = -8. The intercepts are (10, 0) and (0, -8).

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 it rises, negative slope means it falls).

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

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y: y = -A/B * x + C/B.

Parallel lines have the same slope. This means they will never intersect and are always equidistant from each other.