The y intercept of a graph containing the two points (3,1) and (7,-2) is [tex]\frac{13}{4}[/tex]
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:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here the points are (3, 1) and (7, -2)
[tex](x_1, y_1) = (3, 1)\\\\(x_2, y_2) = (7, -2)[/tex]
Substituting in formula, we get
[tex]m = \frac{-2-1}{7-3}\\\\m = \frac{-3}{4}[/tex]
To find the y intercept:
[tex]\text{Substitute } m = \frac{-3}{4} \text{ and } (x, y) = (3, 1) \text{ in eqn 1 }[/tex]
[tex]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}[/tex]
Thus y -intercept is [tex]\frac{13}{4}[/tex]
