Question

Use the information given to find the equation of the line using the point-slope formula (y – y_1) = m(x – x_1). Then convert your answer to slopeintercept form (y = mx + b).y-intercept of 2 and (4,-1)

Answer 1

Using the formula for the slope of a line that passes through two given points we get:

$\begin{gathered} m=\frac{-1-2}{4-0}, \\ m=\frac{-3}{4}, \\ m=-\frac{3}{4}\text{.} \end{gathered}$

Now, using the point-slope formula for the equation of a line we get:

$y-(-1)=-\frac{3}{4}(x-4)\text{.}$

Taking the above equation to its slope-intercept form we get:

$\begin{gathered} y+1=-\frac{3}{4}x-\frac{3}{4}(-4), \\ y=-\frac{3}{4}x+3-1, \\ y=-\frac{3}{4}x+2 \end{gathered}$

Answer:

The point-slope form is:

$y-(-1)=-\frac{3}{4}(x-4)\text{.}$

The slope-intercept form is:

$y=-\frac{3}{4}x+2.$