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:

$m=\frac{y_2-y_1}{x_2-x_1}$

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

x₁ = -4

y₁ = -1

x₂ = 3

y₂ = 4

Then, we find:

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

So, the equation we found so far is:

$y=\frac{5}{7}x+b$

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

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

Therefore, the answer is:

$y=\frac{5}{7}x+\frac{13}{7}$