How do you write the equation of the line with (1, 7) and (2, 10)?

Question

Eva Adamson · Accepted Answer

#y=3x+4# #"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)=(1,7)" and "(x_2,y_2)=(2,10)# #rArrm=(10-7)/(2-1)=3/1=3# #rArry=3x+blarrcolor(blue)"is the partial equation"# #"to find b substitute either of the 2 given points into"# #"the partial equation"# #"using "(1,7)" then"# #7=3+brArrb=7-3=4# #rArry=3x+4larrcolor(red)"is the equation of line"#

Jameson Allen · Answer

undefined To write the equation of the line passing through the points (1, 7) and (2, 10), you can use the point-slope form:

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

where $ m $ is the slope of the line, and $ (x_1, y_1) $ is one of the given points.

First, calculate the slope using the formula:

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

Substitute the coordinates of the given points into the formula to find the slope.

Then, choose one of the points and substitute its coordinates into the point-slope form along with the calculated slope to get the equation of the line.