229k views
2 votes
How do you solve it WITHOUT using graph paper?

Line A passes through the points (-4, 3) and (-2, -1).
Line B passes through the points (-4, 4) and (-5, 7).
At what point do the lines intersect?

A step by step explanation please!

1 Answer

5 votes

Answer: To find the point of intersection of two lines without using graph paper, we can use the method of solving a system of equations.

First, we need to find the slope-intercept form of each line. The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of Line A, we can use the slope formula: m = (y2 - y1)/(x2 - x1). Plugging in the given points, we get: m = (-1 - 3)/(-2 - (-4)) = -4/2 = -2.

Therefore, Line A can be written as y = -2x + b. To find the y-intercept, b, we can plug in one of the points, such as (-4,3) and solve for b: 3 = -2(-4) + b, so b = 11.

So, the slope-intercept form of Line A is y = -2x + 11

We can use the same process to find the slope-intercept form of Line B: m = (7 - 4)/(-5 - (-4)) = 3/1 = 3. So Line B can be written as y = 3x + b. Plugging in one of the points, (-4,4), we get 4 = 3(-4) + b, so b = 16.

So, the slope-intercept form of Line B is y = 3x + 16

Now we have two equations: y = -2x + 11 and y = 3x + 16. To find the point of intersection, we need to find the values of x and y that make both equations true. To do this, we can set the two equations equal to each other:

-2x + 11 = 3x + 16

Subtracting 3x from both sides:

-5x = 5

Dividing both sides by -5:

x = -1

Now we can substitute this value of x back into either equation to find the corresponding value of y. Using y = -2x + 11:

y = -2(-1) + 11 = -2 + 11 = 9

So the point of intersection of Line A and Line

Explanation:

User WhiteSkar
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories