How do you write an equation of the line that passes through the given points (-7,0), (4,11)?

Question

Kennedy Adams · Accepted Answer

#y= x+7#

The equation of a line can be given as #y = mx +c#

As you have 2 points, you can find the slope:

#m = (y_2-y_1)/(x_2-x_1) = (11-0)/(4- (-7)) = 11/11#

#m = 1#

Now to find a value for #c#, substitute #m# and one of the points #(x,y)# into #y= mx+c#

#m = 1 and (x,y) = (-7,0)#

#0= (1)(-7) +c#

#7=c#

The equation is #y= x+7#

Eva Abramson · Answer

undefined To write the equation of the line passing through the points (-7,0) and (4,11), you can follow these steps:

1. Calculate the slope using the formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $, where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.
2. Once you have the slope $ m $, choose one of the points (let's say (-7,0)) and substitute its coordinates and the slope into the point-slope form of the equation: $ y - y_1 = m(x - x_1) $.
3. Plug in the values and simplify to get the equation in the slope-intercept form $ y = mx + b $, where $ b $ is the y-intercept.

Let's calculate the slope first:

$ m = \frac{11 - 0}{4 - (-7)} $

$ m = \frac{11}{11} $

$ m = 1 $

Now, using the point-slope form with the point (-7,0):

$ y - 0 = 1(x - (-7)) $

$ y = x + 7 $

Therefore, the equation of the line passing through the points (-7,0) and (4,11) is $ y = x + 7 $.