What is the equation of the line passing through #(0,-12)# and #(8,72)#?

Question

Eva Abramson · Accepted Answer

#y=21/2x-12# #"the equation of a line in "color(blue)"slope-intercept form"# is. #•color(white)(x)y=mx+b# #"where m is the slope and b the y-intercept"# #"to calculate m use the "color(blue)"gradient formula"# #•color(white)(x)m=(y_2-y_1)/(x_2-x_1)# #"let "(x_1,y_1)=(0,-12)" and "(x_2,y_2)=(8,72)# #m=(72-(-12))/(8-0)=84/8=21/2# #"note that "b=-12to(0,color(red)(-12))# #y=21/2x-12larrcolor(red)"is the equation of the line"#

Eva Adamson · Answer

undefined To find the equation of the line passing through the points (0, -12) and (8, 72), you first need to determine the slope (m) 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.

Substituting the given points:

$$m = \frac{72 - (-12)}{8 - 0}$$
$$m = \frac{84}{8}$$
$$m = 10.5$$

Now that you have the slope, you can use the point-slope form of a linear equation, which is:

$$y - y_1 = m(x - x_1)$$

Substitute one of the points and the slope into the equation:

$$y - (-12) = 10.5(x - 0)$$
$$y + 12 = 10.5x$$

Now, you can simplify the equation to the slope-intercept form (y = mx + b) by solving for y:

$$y = 10.5x - 12$$

So, the equation of the line passing through the points (0, -12) and (8, 72) is $y = 10.5x - 12$.