How do you write an equation in point slope and slope intercept form given (2, 7) and (-2, 9)?

Question

Eva Abramson · Accepted Answer

#y-7=-1/2(x-2)" and "y=-1/2x+8# #"the equation of a line in "color(blue)"point-slope form"# is. #•color(white)(x)y-y_1=m(x-x_1)# #"where m is the slope and "(x_1,y_1)" a point on the line"# #"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(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))# #"let "(x_1,y_1)=(2,7)" and "(x_2,y_2)=(-2,9)# #rArrm=(9-7)/(-2-2)=2/(-4)=-1/2# #"to obtain the point-slope equation"# #"with "m=-1/2" and "(x_1,y_1)=(2,7)# #y-7=-1/2(x-2)larrcolor(red)"in point-slope form"# #"rearranging into slope-intercept form"# #y-7=-1/2x+1# #rArry=-1/2x+8larrcolor(red)" in slope-intercept form"#

Kennedy Adams · Answer

undefined To write an equation in point-slope form given the points (2, 7) and (-2, 9), you first find the slope using the formula:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$

Substituting the given points:

$$ m = \frac{9 - 7}{-2 - 2} = \frac{2}{-4} = -\frac{1}{2} $$

Then, using one of the points and the slope, you can write the equation in point-slope form:

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

Choosing the point (2, 7):

$$ y - 7 = -\frac{1}{2}(x - 2) $$

To convert this equation into slope-intercept form (y = mx + b), you distribute the slope and solve for y:

$$ y - 7 = -\frac{1}{2}x + 1 $$
$$ y = -\frac{1}{2}x + 1 + 7 $$
$$ y = -\frac{1}{2}x + 8 $$