Answer:
There's two possible answers.
Explanation:
To determine the point of intersection between the line y = -30 and the line passing through the points (14, 90) and (-63, 200), we can equate the y-values of the two lines and solve for the corresponding x-value.
The first line, y = -30, is a horizontal line that always has a y-value of -30 regardless of the x-value.
The second line passing through (14, 90) and (-63, 200) can be expressed using the slope-intercept form of a linear equation:
y - y₁ = m(x - x₁)
where (x₁, y₁) = (14, 90), and m is the slope of the line.
First, let's find the slope (m) using the two points:
m = (y₂ - y₁) / (x₂ - x₁)
m = (200 - 90) / (-63 - 14)
m = 110 / -77
m = -10/7
Now, we can write the equation of the second line:
y - 90 = (-10/7)(x - 14)
y - 90 = (-10/7)x + 140/7
y = (-10/7)x + 20/7
To find the point of intersection, we set the y-values of the two lines equal to each other:
-30 = (-10/7)x + 20/7
Now, let's solve for x:
(-10/7)x = -20/7 + 30
(-10/7)x = 10/7
Multiply both sides by -7/10 to isolate x:
x = (10/7) * (-7/10)
x = -1
Now that we have the x-value, we substitute it back into either of the equations to find the y-value. Let's use the equation y = -30:
y = -30
Therefore, the point of intersection between the line y = -30 and the line passing through (14, 90) and (-63, 200) is (-1, -30).
The second possible answer.
Given:
Point A: (14, 90)
Point B: (-63, 200)
To find the equation of the line passing through these two points, we need to determine the slope (m) first.
m = (y₂ - y₁) / (x₂ - x₁)
m = (200 - 90) / (-63 - 14)
m = 110 / -77
m = -10/7
Now, we can use the point-slope form of the equation to find the line passing through these points:
y - y₁ = m(x - x₁)
Using Point A (14, 90):
y - 90 = (-10/7)(x - 14)
y - 90 = (-10/7)(x) + (10/7)(14)
y - 90 = (-10/7)x + 20
Simplifying the equation:
y = (-10/7)x + 110
Since we are looking for the point of intersection with the line y = -30, we can set the two expressions for y equal to each other and solve for x:
-30 = (-10/7)x + 110
Solving for x:
(-10/7)x = -30 - 110
(-10/7)x = -140
x = (-140) / (-10/7)
x = 98
Now, we substitute the x-value back into either equation to find the corresponding y-value. Let's use the equation y = -30:
y = -30
Therefore, the point of intersection between the line y = -30 and the line passing through (14, 90) and (-63, 200) is (98, -30).