9. Write an equation of a line that passes through (9,-5) and (3,-5). Hint: To answer this question, first find the slope using these 2 points.
10. Write an equation of a line that passes through the points (2,3) and (2,-6).
Hint: To answer this question, first find the slope using
9. Notice the 2 given points lie along a horizontal line
so the equation is simply their height or y = -5
10. Same concept, except this time the two points form a vertical line, (did you notice their x's were the same ? )
so the equation is simply x = 2
To find the equation of a line that passes through two given points, we first need to find the slope of the line using the formula:
slope = (change in y-coordinates)/(change in x-coordinates)
Let's find the slope for the first question:
Point 1: (9, -5)
Point 2: (3, -5)
change in y-coordinates = -5 - (-5) = 0
change in x-coordinates = 3 - 9 = -6
slope = 0 / -6 = 0
The slope is 0.
Now, we can use the slope-intercept form of a linear equation (y = mx + b) to find the equation of the line. We will substitute one of the given points into the equation and solve for the y-intercept (b).
Using the first point (9, -5):
-5 = 0(9) + b
-5 = b
The y-intercept (b) is -5.
Therefore, the equation of the line that passes through (9, -5) and (3, -5) is:
y = 0x - 5
y = -5
Now, let's find the slope for the second question:
Point 1: (2, 3)
Point 2: (2, -6)
change in y-coordinates = -6 - 3 = -9
change in x-coordinates = 2 - 2 = 0
The slope is undefined because we have a zero in the denominator.
Since the slope is undefined, we have a vertical line passing through the points (2, 3) and (2, -6).
So, the equation of the line that passes through (2, 3) and (2, -6) is:
x = 2