Question

6.Here are two points: (-3,4), (1,7). What is the slope of the line between them?4A.33B.4I1C.62D.3

Answer 1

Question:

Here are two points: (-3,4), (1,7). What is the slope of the line between them?

Solution:

The slope-intercept form of a line is given by the following equation:

y = mx + b

where m is the slope of the line, and b is the y-coordinate of the y-intercept. Now, By definition, the slope of the line that passes through two points (X1,Y1) and (X2,Y2) is:

$m\text{ = }\frac{Y2-Y1}{X2-X1}$

in our case, we have that:

(X1, Y1) = (-3,4)

(X2,Y2) = (1,7)

Replacing these points in the slope equation we obtain:

$m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{7-4}{1-(-3)}=\text{ }\frac{7-4}{1-(-3)}=\text{ }\frac{3}{1+3}=\text{ }\frac{3}{4}$

then, the equation of the given line is:

$y\text{ = }\frac{3}{4}x+b$

Now, to find b, replace any point (x,y) of the line, in the above equation. For example, take the point (x,y) = (1,7) and replace it on the above equation:

$7\text{= }\frac{3}{4}\cdot1+b$

this is equivalent to:

$7\text{= }\frac{3}{4}+b$

solve for b:

$b\text{ = 7 - }\frac{3}{4}\text{ = }\frac{25}{4}$

thus, we can conclude that the equation of this line is:

$y\text{ = }\frac{3}{4}x+\text{ }\frac{25}{4}$

And the corresponding graph is:

Then, the correct answer is: A