Question

Write an equation in point-slope form of the line that passes through the given points(1,3) and (-3,0) or with the given characteristics

Answer 1

Answer:

$y=\frac{3}{4}(x+3)$

Explanation:

The point-slope form of the equation of a line is generally given as;

$y-y_1=m(x_{}-x_1)_{}$

where m = slope of the line

x1 and y1 = coordinates of the point.

Let's 1st of all determine the slope of the line that passes through the points with coordinates x1 = 1, x2 = -3, y1 = 3, and y2 = 0 using the below formula;

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-3}{-3-1}=\frac{-3}{-4}=\frac{3}{4}$

Let's go ahead and write the equation of the line in point-slope form using m = 3/4 and x1 = 1 and y1 = 3;

$\begin{gathered} y-3=\frac{3}{4}(x-1) \\ y-3=\frac{3x}{4}-\frac{3}{4} \\ y=\frac{3x}{4}-\frac{3}{4}+3 \\ y=\frac{3x}{4}+\frac{(-3+12)}{4} \\ y=\frac{3x}{4}+\frac{9}{4} \\ y=\frac{3}{4}(x+3) \end{gathered}$