Question

Find the equation of the line passingthrough the points (3, 3) and (4, 5).y=[? ]x + [ ]Enter

Answer 1

To solve the exercise, we can first find the slope of the line using this 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 which the line passes} \end{gathered}`

So, in this case, we have:

`\begin{gathered} (x_1,y_1)=(3,3) \\ (x_2,y_2)=(4,5) \\ m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ m=(5-3)/(4-3) \\ m=(2)/(1) \\ $$\boldsymbol{m=2}$$ \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-3=2(x-3) \\ \text{ Apply the distributive property from both sides of the equation} \\ y-3=2\cdot x-2\cdot3 \\ y-3=2x-6 \\ \text{ Add 3 from both sides of the equation} \\ y-3+3=2x-6+3 \\ y=2x-3 \end{gathered}`

Therefore, the equation of the line passing through the points (3,3) and (4,5) is

`$$\boldsymbol{y=2x-3}$$`