Question

Which of the following equation represents a line through the points?

Answer 1

To solve the exercise, we can first find the slope of the line that passes through the given points using the following formula:

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ \text{ Where m is the slope and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through the line passes} \end{gathered}`

So, in this case, we have:

`\begin{gathered} (x_1,y_1)=(1,2) \\ (x_2,y_2)=(2,5) \\ m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ m=(5-2)/(2-1) \\ m=(3)/(1) \\ m=3 \end{gathered}`

Now, we can use the point-slope formula to find the equation of the line in its slope-intercept form:

`\begin{gathered} y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula} \\ y-2=3(x-1) \\ \text{ Apply the distributive property to the left side of the equation} \\ y-2=3\cdot x-3\cdot1 \\ y-2=3x-3 \\ \text{ Add 2 from both sides of the equation} \\ y-2+2=3x-3+2 \\ y=3x-1 \end{gathered}`

Therefore, the equation that represents the line that passes through the given points is

`$$\boldsymbol{y=3x-1}$$`