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{ = }(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{ = }(Y2-Y1)/(X2-X1)=\text{ }(7-4)/(1-(-3))=\text{ }(7-4)/(1-(-3))=\text{ }(3)/(1+3)=\text{ }(3)/(4)`

then, the equation of the given line is:

`y\text{ = }(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{= }(3)/(4)\cdot1+b`

this is equivalent to:

`7\text{= }(3)/(4)+b`

solve for b:

`b\text{ = 7 - }(3)/(4)\text{ = }(25)/(4)`

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

`y\text{ = }(3)/(4)x+\text{ }(25)/(4)`

And the corresponding graph is:

Then, the correct answer is: A