Question

Write an equation in slope-intercept form of the line that passes through
(7, 2) and (2, 12).

Answer 1

The equation in slope-intercept form of the line passing through the given points is $y = -5x + 37$

Given the following points:

• Points on the x-axis = (7, 2)

• Points on the y-axis = (2, 12)

To write an equation in slope-intercept form of the line passing through the given points, we would use the following formula;

$Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the points into the formula, we have;

$Slope. \;m = \frac{12\; - \;2}{2\; - \;7}\\\\Slope. \;m = \frac{10}{-5}$

Slope, m = -5

Next, we would find the intercept:

The standard form of an equation of line is given by the formula;

$y = mx + b$

Where:

• x and y are the points.

• m is the slope.

• b is the intercept.

Substituting the values, we have:

$2 = -5(7) + b\\\\2 = -35 + b\\\\b = 35 + 2$

b = 37

Now, we would write the equation in slope-intercept form:

$y = -5x + 37$

Therefore, the equation in slope-intercept form of the line passing through the given points is $y = -5x + 37$

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Answer 2

Answer:

Step-by-step explanation:

(12 - 2)/(2 - 7)= 10/-5= -2

y - 2 = -2(x - 7)

y - 2 = -2x + 14

y = -2x + 16