write an equation in slope-intercept form of the line that passes through the given points.
a. (-6,1), (3,-7)
b. (-2/3,4), (6, -1/3)
write an equation in point-slope form of the line that passes through the given poitns.
c. (-2,5), (4,-3)
d. (1/2,-1), (-2/3,6)
plz show me how to do these.. thnxxxx
a. y = -8x/3 + 1
b. y = -13x/20 + 107/30
c. y + 3 = (-4/3)(x + 2)
d. y + 1 = -6x + 3
are these correct?
Equation that represents the line that passes through the points (-3,7)and (3,3)
To find the equation of a line that passes through two given points, you can use either the slope-intercept form or the point-slope form. I'll explain how to do both for each set of points.
a. (-6,1), (3,-7)
Using the slope-intercept form (y = mx + b):
1. Find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
Substituting the coordinates: m = (-7 - 1) / (3 - (-6)) = -8 / 9
2. Choose one of the points (let's use (-6,1)) and substitute its coordinates into the equation: y = mx + b
1 = (-8 / 9)(-6) + b
Simplifying, we get: 1 = 48 / 9 + b
3. Solve for b (the y-intercept) by isolating b:
1 - (48 / 9) = b
Simplifying, we get: b = -41 / 9
4. The equation of the line is: y = (-8 / 9)x - 41 / 9
Using the point-slope form (y - y1 = m(x - x1)):
1. Find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
Substituting the coordinates: m = (-7 - 1) / (3 - (-6)) = -8 / 9
2. Choose one of the points (let's use (-6,1)) and substitute its coordinates into the equation: y - y1 = m(x - x1)
y - 1 = (-8 / 9)(x - (-6))
3. Simplify and rearrange the equation: y - 1 = (-8 / 9)(x + 6)
4. The equation of the line is: y - 1 = (-8 / 9)(x + 6)
b. (-2/3,4), (6, -1/3)
Using the slope-intercept form (y = mx + b):
1. Find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
Substituting the coordinates: m = (-1/3 - 4) / (6 - (-2/3)) = -19/26
2. Choose one of the points (let's use (-2/3,4)) and substitute its coordinates into the equation: y = mx + b
4 = (-19/26)(-2/3) + b
Simplifying, we get: 4 = 38/78 + b
3. Solve for b (the y-intercept) by isolating b:
4 - (38/78) = b
Simplifying, we get: b = 120/78
4. The equation of the line is: y = (-19/26)x + 120/78, which can be simplified to y = (-19/26)x + 20/13
Using the point-slope form (y - y1 = m(x - x1)):
1. Find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
Substituting the coordinates: m = (-1/3 - 4) / (6 - (-2/3)) = -19/26
2. Choose one of the points (let's use (-2/3,4)) and substitute its coordinates into the equation: y - y1 = m(x - x1)
y - 4 = (-19/26)(x - (-2/3))
3. Simplify and rearrange the equation: y - 4 = (-19/26)(x + 2/3)
4. The equation of the line is: y - 4 = (-19/26)(x + 2/3)