The equations \(y = x + 3\) and \(-4x + 4y = 28\) (which simplifies to \(y = x + 7\)) are both in slope-intercept form with a slope of 1. This means for each unit increase in \(x\), \(y\) increases by 1. The first line has a y-intercept at (0, 3) and the second at (0, 7), indicating they are parallel and do not intersect. The first line remains consistently below the second line across the graph, maintaining a constant distance apart.
Equation 1: y=x+3 This is already in slope-intercept form y=mx+b where m (slope) is 1 and b (y-intercept) is 3. The slope indicates that for every unit increase in x, y increases by 1. The y-intercept indicates that the line crosses the y-axis at .(0, 3) To plot this, you can choose other points like: when x=0, y=3 (point(0.3)) When x=2, y=5 (point(2,5)) when x=-3, y=0 (point(-3,0)
Equation 2: -4x+4y=28 First, let's convert this to slope-intercept form. We can do this by solving for y 4y=4x+28 y=x+7 This equation is also in the form y=mx+b where m=1 and b=7 . Similar to the first equation, this line also has a slope of 1. The y-intercept is 7, meaning the line crosses the y-axis at (0,7) You can find additional points to plot: When x=0, y=7 (point (0,7)) When x=2, y=9 (point (2,9)) When x= -3, y=4 (point -4, 4)) Graphing the Lines: Both lines have the same slope one, which means they are parallel lines. The first line (from y=x+3) has a lower y-intercept and thus is always below the second line (from y=x+7) at any given point x Summary of the Graph: Both lines are straight and have a slope of 1, indicating they rise at the same angle from left to right. The first line will intersect the y-axis at (0, 3) and the second line at (0, 7). The lines do not intersect since they are parallel and maintain a constant distance apart. This information can be used to sketch a graph showing these two parallel lines, providing a visual representation of their relationship.
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