Question

find the equation of the line passing through the given pair of points. Write the equation in slope intercept form(-4,-1),(3,4)what is the slope intercept form of the equation that passes through (-4,-1) (3,4?)

Answer 1

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

`y=mx+b`

where m is the slope and b is the y-intercept.

We can find the slope m of a line passing through points (x₁,y₁) and (x₂,y₂) using the formula:

`m=(y_2-y_1)/(x_2-x_1)`

Thus, for the points (-4,-1) and (3,4), we have:

x₁ = -4

y₁ = -1

x₂ = 3

y₂ = 4

Then, we find:

`\begin{gathered} m=(4-(-1))/(3-(-4)) \\ \\ m=(4+1)/(3+4) \\ \\ m=(5)/(7) \end{gathered}`

So, the equation we found so far is:

`y=(5)/(7)x+b`

Now, we can find the value of b by replacing x and y with the coordinates of the point (3,4):

`\begin{gathered} 4=(5)/(7)(3)+b \\ \\ 4\cdot7=(15)/(7)\cdot7+7b \\ \\ 28=15+7b \\ \\ 7b=28-15 \\ \\ b=(13)/(7) \end{gathered}`

Therefore, the answer is:

`y=(5)/(7)x+(13)/(7)`