Question

What is the slope-intercept form equation of the line that passes through (2, 4) and (4, 10)?

y = −3x − 2

y = −3x + 2

y = 3x + 2

y = 3x − 2

Answer 1

well first you would have to find the slopes of the 2 coordinates (2, 4) and (4, 10). Do u know how to find the slope?

Answer 2

\[slope = m = \frac{ y _{2}- y _{1} }{ x _{2}-x _{1} }\]

Answer 3

\[m = \frac{ 10 - 4 }{ 4-2 } = \frac{ 6 }{ 2 } = 3\]

Answer 4

so, the slope is 3. m= 3 in \[y = mx + b\]

Answer 5

Automatically, the first and second options to the question are out because the slope there is -3 instead of 3.

Answer 6

Now, you can use any of the two coordinates (2, 4) or (4, 10) to substitute for y and x in order to find b. Let's choose (2, 4).

Answer 7

\[y = 3x + b\]
substitute 2 for x and 4 for y to the above equation because (2, 4) is equal to (x, y)
\[4 = 3(2) + b \]
\[4 = 6 + b\]
solve for b.

4 = 6 + b
-6 -6
----------
b = -2

Answer 8

Now you found out what m is equal to and what b is equal in order to write the slope-intercept form.
So, this is the answer: the last option
\[y = 3x -2\]

Answer 9

thank you!