Find a linear equation whose graph is the straight line with the given property. HINT [See Example 2.]
Through (2, −3) and (1, 1)
Which formula do I use?
y2-y1/x2-x1 or y-y1=m(x-x1)[<--if i use this how do i plug in the numbers?]
Thank you.
Use both formulas.
m = (y2 - y1)/(x2 - x1)
= [1 - (-3)]/(1 - 2)
= (1 + 3)/(1 - 2)
= 4/-1 or -1/4
Substitute the first ordered pair into the second formula:
y - (-3) = -1/4(x - 2)
y + 3 = -1/4x + 2/4
y = -1/4x + 2/4 - 3
y = -1/4x - 10/4
This equation is in the form: y = mx+b
I hope this helps.
To find a linear equation given two points, you can use the formula:
y - y1 = m(x - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, you have the points (2, -3) and (1, 1).
To find the equation, you need to calculate the slope (m) first:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the given points:
m = (1 - (-3)) / (1 - 2)
= 4 / -1
= -4
Now, you can choose any of the two points (2, -3) or (1, 1) to substitute into the equation. Let's choose (2, -3):
y - (-3) = -4(x - 2)
Simplifying:
y + 3 = -4x + 8
Finally, rearrange the equation to standard form:
4x + y = 5
So, the linear equation that satisfies the given condition is 4x + y = 5.
To find a linear equation that represents a straight line passing through two given points, you can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.
To determine the slope (m), you can use the formula:
m = (y2 - y1) / (x2 - x1)
Given that the two points are (2, -3) and (1, 1), you can substitute the coordinates into the formula:
m = (1 - (-3)) / (1 - 2) = 4 / -1 = -4
Now that you have the slope, you need to find the y-intercept (b). You can choose either of the two points to substitute into the equation: y = mx + b.
Let's use the point (2, -3):
-3 = -4(2) + b
-3 = -8 + b
b = -3 + 8
b = 5
So the equation of the line that passes through the points (2, -3) and (1, 1) is y = -4x + 5.