Question

Line passing through (0, 9) , (8, 7)

Answer 1

We are given:

The 2 points through which the line passes through

(0,9) and (8,7)

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Finding the equation of the line:

To find the equation of the line, we will use the slope-intercept form:

y = mx + b           [where m is the slope and b is the y-intercept]

So, we need the slope and the y-intercept of the line in order to find the equation

Finding the slope:

We know that the slope of a line is:  change in y / change in x

So, Slope = $\frac{y_{2} - y_{1} }{x_{2} - x_{1}}$

replacing the variables:

Slope = (7-9) / (8-0)

Slope =  -2 / 8

Slope = -1/4

Finding the y-intercept:

Since we know the slope, we know that the equation of the line will look like:

y=  (-1/4)x + b              [where b is the y-intercept]

we know that the ordered pair (0,9) will satisfy the equation since the line passes through that point

So, y = 9 and x = 0 will satisfy the equation:

9 = (-1/4)(0) + b

b = 9

Hence, the y-intercept is 9

Equation of the line:

We know that the general form of the slope-intercept form is:

y = mx + b                [where m is the slope and b is the y-intercept]

Since we know the values of the slope and the y-intercept:

y = (-1/4)x + 9

y = -x/4 + 9 is the equation of the line that passes through the given points