How do you find the equation of the line passing through the points (1,4) and (-2,6)?

Question

Eva Abramson · Accepted Answer

#y=-2/3x+14/3# #"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)=(1,4)" and "(x_2,y_2)=(-2,6)# #rArrm=(6-4)/(-2-1)=2/(-3)=-2/3# #rArry=-2/3x+blarrcolor(blue)"is the partial equation"# #"to find b substitute either of the 2 given points into"# #"the partial equation"# #"using "(1,4)" then"# #4=-2/3+brArrb=12/3+2/3=14/3# #rArry=-2/3x+14/3larrcolor(red)"equation of line"#

Abigail Allen · Answer

undefined To find the equation of the line passing through the points (1,4) and (-2,6), you can use the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of one point, and m is the slope.

1. Calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
2. Choose one of the points and plug its coordinates into the equation.
3. Substitute the slope and the chosen point's coordinates into the point-slope form equation.
4. Simplify the equation to get it in slope-intercept form (y = mx + b), if necessary.

Jameson Allen · Answer

undefined To find the equation of the line passing through the points (1, 4) and (-2, 6), you first 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.

Substituting the given points:

$$ m = \frac{6 - 4}{-2 - 1} = \frac{2}{-3} $$

Next, you use the point-slope form of the equation of a line, which is:

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

Choose one of the given points (either (1, 4) or (-2, 6)) and substitute its coordinates as $ x_1 $ and $ y_1 $, and then substitute the calculated slope as $ m $.

Let's use point (1, 4):

$$ y - 4 = \frac{2}{-3}(x - 1) $$

Now, you can simplify this equation to put it in slope-intercept form (y = mx + b), where $ b $ is the y-intercept:

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

$$ y = \frac{2}{-3}x + \frac{14}{3} $$

This is the equation of the line passing through the points (1, 4) and (-2, 6).