What is the equation of the line passing through #(1,3), (4,6)#?
2 Answers
Explanation:
#"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)=(1,3)" and "(x_2,y_2)=(4,6)#
#rArrm=(6-3)/(4-1)=3/3=1#
#rArry=x+blarrcolor(blue)"is the partial equation"#
#"to find b substitute either of the 2 given points into"#
#"the partial equation"#
#"using "(1,3)" then"#
#3=1+brArrb=3-1=2#
#rArry=x+2larrcolor(red)"is the equation of the line"#
Explanation:
First, we must know what an equation of a line looks like. We write the equation in slope-intercept form:
(The
Next, find the slope (
Next, find the y-intercept (
-OR-
Now, we can write the full equation of the line:
(We do not need to put a