Math

QuestionFind the point of intersection or graph the lines y=2x7y=2x-7 and y=2x+13y=2x+13. What should be done?

Studdy Solution

STEP 1

Assumptions1. We have two linear equations y=x7y=x-7 and y=x+13y=x+13 . The equations are in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept3. We are trying to analyze these equations

STEP 2

First, we notice that the slopes of both equations are the same (m =2). This means that the lines are parallel to each other.
m1=m2=2m1 = m2 =2

STEP 3

Next, we look at the y-intercepts of the two equations. The y-intercept of the first equation is -7 and the y-intercept of the second equation is13.
b1=7,b2=13b1 = -7, b2 =13

STEP 4

Since the slopes are equal and the y-intercepts are different, we can conclude that these two lines are parallel and will never intersect.

STEP 5

If we were asked to graph these equations, we would plot the y-intercepts on the y-axis and then use the slope to find another point on each line. Since the slope is2, we would go up2 units and over1 unit from the y-intercept to find another point.

STEP 6

If we were asked to find the point of intersection, we would set the two equations equal to each other and solve for x. However, since these lines are parallel, they will never intersect and there is no solution to the system of equations.
In conclusion, without a specific task given, we can only analyze these equations and say that they represent two parallel lines with different y-intercepts. If we were asked to graph them, we could do so. If we were asked to find a point of intersection, we would say there is no such point.

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