Math  /  Algebra

Question6) Write the equation of the line in slope-intercept form through the points (2,1)(-2,-1) and (1,7)(1,-7).

Studdy Solution

STEP 1

1. We need to find the equation of a line in slope-intercept form.
2. The line passes through the points (2,1)(-2, -1) and (1,7) (1, -7) .
3. Slope-intercept form of a line is given by y=mx+b y = mx + b , where m m is the slope and b b is the y-intercept.

STEP 2

1. Calculate the slope of the line using the given points.
2. Use the slope and one of the points to solve for the y-intercept.
3. Write the equation of the line in slope-intercept form.

STEP 3

Calculate the slope of the line using the formula for slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (2,1)(-2, -1) and (1,7) (1, -7) :
m=7(1)1(2) m = \frac{-7 - (-1)}{1 - (-2)} m=7+11+2 m = \frac{-7 + 1}{1 + 2} m=63 m = \frac{-6}{3} m=2 m = -2

STEP 4

Use the slope m=2 m = -2 and one of the points, say (2,1)(-2, -1), to find the y-intercept b b .
Substitute into the slope-intercept form y=mx+b y = mx + b :
1=2(2)+b -1 = -2(-2) + b 1=4+b -1 = 4 + b
Solve for b b :
b=14 b = -1 - 4 b=5 b = -5

STEP 5

Write the equation of the line in slope-intercept form using the slope m=2 m = -2 and y-intercept b=5 b = -5 :
y=2x5 y = -2x - 5

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