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Math  /  Algebra

QuestionQuestion What is an equation of the line that passes through the points (1,−4)(1, -4) and (−1,6)(-1, 6)? Answer Attempt 1 out of 2 Submit Answer Watch Video Show Examples

Studdy Solution

STEP 1

1. We are given two points: (1,−4)(1, -4) and (−1,6)(-1, 6).
2. We need to find the equation of the line that passes through these two points.
3. The equation of a line can be expressed in the slope-intercept form: 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 find 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 the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (1,−4)(1, -4) and (−1,6)(-1, 6) into the formula:
m=6−(−4)−1−1 m = \frac{6 - (-4)}{-1 - 1} m=6+4−2 m = \frac{6 + 4}{-2} m=10−2 m = \frac{10}{-2} m=−5 m = -5

STEP 4

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

STEP 5

Write the equation of the line in slope-intercept form using the slope m=−5 m = -5 and y-intercept b=1 b = 1 :
y=−5x+1 y = -5x + 1

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