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 $\frac{13}{4}$

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:

$m = \frac{y_2-y_1}{x_2-x_1}$

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

$m = \frac{-2-1}{7-3}\\\\m = \frac{-3}{4}$

To find the y intercept:

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

$1 = \frac{-3}{4} \times 3 + c\\\\1 = \frac{-9}{4} + c\\\\ \text{Simplify the above equation } \\\\1 = \frac{-9+4c}{4}\\\\4 = -9 + 4c\\\\13 = 4c\\\\\text{Divide both sides by 4 }\\\\c = \frac{13}{4}$

Thus  y -intercept is $\frac{13}{4}$