Which equation describes the line that contains the points (-5, 2) and (3, 7)?
slope = (7-2)/(3-(-5))
= 5/8
y-7 = (5/8)(x-3)
8y-56 = 5x - 15
-5x + 8y = 41
5x - 8y = -41 in standard form
5x - 8y + 41 = 0 in general form
y = (5/8)x + 41/8 in slope - yintercept form
To find the equation of a line that contains two given points, we can use the slope-intercept form of a line, which is given by:
y = mx + b
Where:
m is the slope of the line, and
b is the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope using the given points:
m = (7 - 2) / (3 - (-5))
= 5 / 8
Now that we have the slope (m), we can substitute one of the points and the slope into the slope-intercept form to find the y-intercept (b).
Using the point (-5, 2):
2 = (5/8)(-5) + b
2 = -25/8 + b
16/8 + 25/8 = b
41/8 = b
So the y-intercept (b) is 41/8.
Therefore, the equation of the line that contains the points (-5, 2) and (3, 7) is:
y = (5/8)x + 41/8
To find the equation of the line that contains the points (-5, 2) and (3, 7), we can use the point-slope equation of a line.
The point-slope equation is given by:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of a point on the line, and m is the slope of the line.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-5, 2) and (x2, y2) = (3, 7).
Substituting the values into the formula, we have:
m = (7 - 2) / (3 - (-5))
= 5 / 8
Now that we have the slope (m), we can choose any point on the line, for example, (-5, 2), and substitute the values into the point-slope equation:
y - 2 = (5/8)(x - (-5))
Simplifying,
y - 2 = 5/8 (x + 5)
Multiplying both sides of the equation by 8 to eliminate the fraction, we get:
8(y - 2) = 5(x + 5)
Expanding,
8y - 16 = 5x + 25
Rearranging the equation to the slope-intercept form (y = mx + b), we have:
8y = 5x + 41
Dividing both sides of the equation by 8,
y = (5/8)x + 41/8
Therefore, the equation of the line that contains the points (-5, 2) and (3, 7) is y = (5/8)x + 41/8.