Question

What is the y intercept of a graph containing the two points (3,1) and (7,-2)?

Answer 1

The y intercept of a graph containing the two points (3,1) and (7,-2) is
`(13)/(4)`

Solution:

Given points are (3, 1) and (7, -2)

The equation of line in slope intercept form is given as:

y = mx + c ------- eqn 1

Where, "m" is the slope of line and "c" is the y intercept

Let us first find the slope of line

The slope of line is given as:

`m = (y_2-y_1)/(x_2-x_1)`

Here the points are (3, 1) and (7, -2)

`(x_1, y_1) = (3, 1)\\\\(x_2, y_2) = (7, -2)`

Substituting in formula, we get

`m = (-2-1)/(7-3)\\\\m = (-3)/(4)`

To find the y intercept:

`\text{Substitute } m = (-3)/(4) \text{ and } (x, y) = (3, 1) \text{ in eqn 1 }`

`1 = (-3)/(4) * 3 + c\\\\1 = (-9)/(4) + c\\\\ \text{Simplify the above equation } \\\\1 = (-9+4c)/(4)\\\\4 = -9 + 4c\\\\13 = 4c\\\\\text{Divide both sides by 4 }\\\\c = (13)/(4)`

Thus y -intercept is
`(13)/(4)`