RTCNTC said:Find an equation of the line that passes through (6, 2) and has the same slope as the line 3x + 4y = 12.
1. Solve the given equation for y. The coefficient of x is the slope.
Yes?
RTCNTC said:2. I then plug the slope and given point into the point-slope formula and solve for y.
True?
The equation of a line is a mathematical representation of a straight line on a graph. It is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of a line, you need to have two points on the line. Then, you can use the slope formula (m = (y2 - y1) / (x2 - x1)) to find the slope. Finally, plug the slope and one of the points into the point-slope formula (y - y1 = m(x - x1)) to get the equation of the line.
The slope represents the rate of change of the line. It tells us how much the y-value changes for every one unit increase in the x-value. The y-intercept represents the point where the line crosses the y-axis.
Yes, the slope of a line can be positive, negative, or zero. A negative slope indicates a downward trend, while a positive slope indicates an upward trend.
The slope-intercept form (y = mx + b) is easier to use and interpret because the slope and y-intercept are explicitly stated. The standard form (Ax + By = C) is useful for graphing and finding the x and y intercepts, but it is not as intuitive as the slope-intercept form.