To intersect, their slopes have to be different. The y-intercept can be anything.
NO they can't
No, vertical lines have an undefined slope.
The slope is the the same, Yet The y-intercept is not the same
Converting from point-slope to slope-intercept form is helpful when you want to easily identify the y-intercept of a linear equation, making it simpler to graph the line. Slope-intercept form ((y = mx + b)) clearly shows the slope ((m)) and the y-intercept ((b)), facilitating quick analysis and comparisons with other lines. This conversion is particularly useful in applications involving linear models or when analyzing intersections with other lines.
For two dimensional lines: Get the formulas for the two lines into a format so that you can evaluate the slope. If the slopes are different, then they will intersect. If the slopes are the same, then you have two parallel lines, or possibly, the two equations describe the same line.
Two linear equations (or lines) with the same y-intercept and different slopes are intersecting lines. They intersect at the y-intercept. If the slopes are negative reciprocals (ex: one slope is 3 and one slope it -1/3) then they are perpendicular lines.
No. In order to be parallel, two lines would have to have the same slope, and different intercepts.Why? Two lines with different slopes, but the same intercepts would result in two intersecting lines. Two lines with the same slope, and the same intercept would result in the same line. Two lines with the same slope, and different intercepts would be parallel.
NO they can't
NO they can't
Intersecting lines NEVER have the same slope. However, if the lines are identical, meaning all their points are the same, then they will, of course, have the same slope as well as everything else. On the other hand, parallel lines have the same slope, but they do not share a single point.
No, vertical lines have an undefined slope.
parallel lines.
The slope is the the same, Yet The y-intercept is not the same
Are equal but the y intercept is different
Parallel lines have the same slope, which makes them parallel. However, they cannot have the same y intercept, or else it would be the same line.
Converting from point-slope to slope-intercept form is helpful when you want to easily identify the y-intercept of a linear equation, making it simpler to graph the line. Slope-intercept form ((y = mx + b)) clearly shows the slope ((m)) and the y-intercept ((b)), facilitating quick analysis and comparisons with other lines. This conversion is particularly useful in applications involving linear models or when analyzing intersections with other lines.
They have the same slope. If you write the lines in the slope-intercept form, you will get, for each line: y = ax + b where a is the slope, and b is the y-intercept (where the line crosses the y-axis). For two or more parallel lines, the coefficient "a" will be the same.