Question

What method can be used to write the equation of a line in slope-intercept form given two points? Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope. Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.

Answer 1

To write the equation of a line in slope-intercept form: A. Find the slope using $m = \frac{y_2 - y_1}{x_2 - x_1}$, and then substitute one point and the slope into the equation $y = m x + b$ to find the y-intercept (b).

What is the Slope-intercept Form Equation of a Line?

The slope-intercept form equation for a given line is expressed as, y = mx + b, where m is the slope and b is the y-intercept.

For example, if we are given two points, say (3, -5) and (-2, 5), first, find the slope:

Slope (m) = y2 - y1/x2 - x1 = (5 -(-5))/(-2 - 3) = 10/-5

m = -2

Next, substitute one point, (-2, 5) and the slope (m), -2, into y = mx + b to find the y-intercept (b):

5 = -2(-2) + b

5 = 4 + b

5 - 4 = b

1 = b

b = 1

Then write the equation in slope-intercept form by substituting m = -2 and b = 1 into y = mx + b:

y = -2x + 1

Therefore, the method to use is: A. Find the slope using $m = \frac{y_2 - y_1}{x_2 - x_1}$, and then substitute one point and the slope into the equation $y = m x + b$ to find the y-intercept (b).

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