# Complete the equation of the line through (2, 1) and (5, -8). Use exact numbers.

Question
Linear equations and graphs
Complete the equation of the line through (2, 1) and (5, -8). Use exact numbers.

2021-02-17
First, we find the slope: $$\displaystyle{m}=\frac{{{y}{2}-{y}{1}}}{{{x}{2}-{x}{1}}}=\frac{{-{8}-{1}}}{{{5}-{2}}}=-\frac{{9}}{{3}}=-{3}$$
Use the slope-intercept form of a line and substitute the slope and a point, say (2,1) to find b: y=mx+b
1=-3(2)+b
1=-6+b
7=b
So, the equation of the linear function is y=-3x+7

### Relevant Questions

A line passes through the point (2, 1) and has a slope of $$\frac{-3}{5}$$.
What is an equation of the line?
A.$$y-1=\frac{-3}{5}(x-2)$$
B.$$y-1=\frac{-5}{3}(x-2)$$
C.$$y-2=\frac{-3}{5}(x-1)$$
D.$$y-2=\frac{-5}{3}(x-1)$$
Write the equation of a line perpendicular to $$\displaystyle{y}=\frac{{1}}{{4}}{x}-{5}$$ that passes through the point (-1,2)
Find the value of r so the line that passes through each pair of points has the given slope. (r, -5), (3, 13), m = 8
a. Use a graphing calculator to find the equation of the line of best fit for the data below. Let x=8 represent 1998, x=9 represent 1999, and so on.
b. What is the slope of the line of best fit? What does the slope mean in terms of the number of computer and video game units sold?
c. What is the y-intercept of the line of best fit? What does the y-intercept mean in terms of the number of computer and viedo game units sold?
Give the equation of the line perpendicular to the line described and satisfying the given conditions. $$\displaystyle{y}=-{\left(\frac{{4}}{{3}}\right)}{x}+{5}$$ with y-intercept (0, -8)
Find an equation in standard form of the line passing through (- 3, - 1) with slope 3.
Given linear equation y = -8-4x
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
Given linear equation y = -0.75x-5
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.