write an equation in point - slope form of the line that passes through the given points , then write the equation in the slope intercept form (-9,7),(9,1)
the slope m = (1-7)/(9+9) = -1/3
so the point-slope form is
y-1 = -1/3 (x-9)
and proceed from there.
To find the equation of a line in point-slope form, we will use the formula:
y - y1 = m(x - x1)
Given points: (-9, 7) and (9, 1)
Step 1: Calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
Using the points (-9, 7) and (9, 1):
m = (1 - 7) / (9 - (-9))
m = -6 / 18
m = -1/3
Step 2: Choose one of the given points (let's use (-9, 7)) and substitute its coordinates and the calculated slope into the point-slope formula:
y - y1 = m(x - x1)
y - 7 = (-1/3)(x - (-9))
Step 3: Simplify the equation:
y - 7 = (-1/3)(x + 9)
y - 7 = (-1/3)x - 3
y = (-1/3)x + 4
The equation of the line in point-slope form is: y - 7 = (-1/3)(x + 9)
To convert it to slope-intercept form, y = mx + b, where b is the y-intercept, we can simplify the equation:
y = (-1/3)x + 4
So, the equation of the line in slope-intercept form is: y = (-1/3)x + 4.
To find the equation of a line in point-slope form, you need two pieces of information: a point on the line and the slope of the line.
Given two points (-9, 7) and (9, 1), let's calculate the slope first.
Slope (m) is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the two points:
m = (1 - 7) / (9 - (-9))
m = -6 / 18
m = -1/3
Now that we have the slope (m), we can use point-slope form which is:
y - y1 = m(x - x1)
Substituting the values of one point (-9, 7) and the slope (-1/3):
y - 7 = (-1/3)(x - (-9))
y - 7 = (-1/3)(x + 9)
To convert this equation to slope-intercept form (y = mx + b), we can simplify it further:
distributing the negative 1/3:
y - 7 = (-1/3)(x) - 3
y - 7 = -x/3 - 3
Now, let's move the term with 'y' to the other side:
y = -x/3 - 3 + 7
y = -x/3 + 4
Therefore, the equation of the line passing through the given points (-9, 7) and (9, 1) in point-slope form is:
y - 7 = (-1/3)(x + 9)
And the equation in slope-intercept form is:
y = -x/3 + 4