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: