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
To write an equation of parallel lines in slope-intercept form (y = mx + b), first identify the slope (m) of the line you want to be parallel to, as parallel lines have the same slope. Then, choose a y-intercept (b) for the new line—this can be any value. Substitute the slope and the chosen y-intercept into the slope-intercept form to get the equation of the parallel line. For example, if the original line is y = 2x + 3, a parallel line could be y = 2x + 1.
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.
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
To write an equation of parallel lines in slope-intercept form (y = mx + b), first identify the slope (m) of the line you want to be parallel to, as parallel lines have the same slope. Then, choose a y-intercept (b) for the new line—this can be any value. Substitute the slope and the chosen y-intercept into the slope-intercept form to get the equation of the parallel line. For example, if the original line is y = 2x + 3, a parallel line could be y = 2x + 1.
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.